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Montcho Y, Dako S, Salako VK, Tovissodé CF, Wolkewitz M, Glèlè Kakaï R. Assessing marginal effects of non-pharmaceutical interventions on the transmission of SARS-CoV-2 across Africa: a hybrid modeling study. MATHEMATICAL MEDICINE AND BIOLOGY : A JOURNAL OF THE IMA 2024; 41:225-249. [PMID: 39083019 DOI: 10.1093/imammb/dqae013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Revised: 07/19/2024] [Accepted: 07/30/2024] [Indexed: 09/18/2024]
Abstract
Since 2019, a new strain of coronavirus has challenged global health systems. Due its fragile healthcare systems, Africa was predicted to be the most affected continent. However, past experiences of African countries with epidemics and other factors, including actions taken by governments, have contributed to reducing the spread of SARS-CoV-2. This study aims to assess the marginal impact of non-pharmaceutical interventions in fifteen African countries during the pre-vaccination period. To describe the transmission dynamics and control of SARS-CoV-2 spread, an extended time-dependent SEIR model was used. The transmission rate of each infectious stage was obtained using a logistic model with NPI intensity as a covariate. The results revealed that the effects of NPIs varied between countries. Overall, restrictive measures related to assembly had, in most countries, the largest reducing effects on the pre-symptomatic and mild transmission, while the transmission by severe individuals is influenced by privacy measures (more than $10\%$). Countries should develop efficient alternatives to assembly restrictions to preserve the economic sector. This involves e.g. training in digital tools and strengthening digital infrastructures.
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Affiliation(s)
- Yvette Montcho
- Laboratoire de Biomathématiques et d'Estimations Forestières, Universty of Abomey-Calavi, 04 BP 1525, Cotonou, Benin
| | - Sidoine Dako
- Laboratoire de Biomathématiques et d'Estimations Forestières, Universty of Abomey-Calavi, 04 BP 1525, Cotonou, Benin
| | - Valère Kolawole Salako
- Laboratoire de Biomathématiques et d'Estimations Forestières, Universty of Abomey-Calavi, 04 BP 1525, Cotonou, Benin
| | - Chénangnon Frédéric Tovissodé
- Laboratoire de Biomathématiques et d'Estimations Forestières, Universty of Abomey-Calavi, 04 BP 1525, Cotonou, Benin
| | - Martin Wolkewitz
- Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, 79104, Freiburg, Germany
| | - Romain Glèlè Kakaï
- Laboratoire de Biomathématiques et d'Estimations Forestières, Universty of Abomey-Calavi, 04 BP 1525, Cotonou, Benin
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2
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Wang Y, Liang Z, Qing S, Liu X, Xu C. Application of an ARFIMA Model to Estimate Hepatitis C Epidemics in Henan, China. Am J Trop Med Hyg 2024; 110:404-411. [PMID: 38190747 PMCID: PMC10859795 DOI: 10.4269/ajtmh.23-0561] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Accepted: 10/11/2023] [Indexed: 01/10/2024] Open
Abstract
Hepatitis C (HC) presents a substantial burden, and a goal has been established for ending HC epidemics by 2030. This study aimed to monitor HC epidemics by designing a paradigmatic autoregressive fractionally integrated moving average (ARFIMA) for projections until 2030, and evaluating its efficacy compared with the autoregressive integrated moving average (ARIMA). Monthly HC incidence data in Henan from January 2004 to June 2023 were obtained. Two periods (January 2004 to June 2022 and January 2004 to December 2015) were treated as training sets to build both models, whereas the remaining periods served as test sets to perform performance evaluation. There were 465,196 HC cases, with an escalation in incidence (average annual percentage change = 8.64, 95% CI: 3.71-13.80) and a peak in March and a trough in February. For both the 12 and 90 holdout data forecasts, ARFIMA generated lower errors than ARIMA across various metrics: mean absolute deviation (252.93 versus 262.28 and 235.37 versus 1,689.65), mean absolute percentage error (0.17 versus 0.18 and 0.14 versus 0.87), root mean square error (350.31 versus 362.31 and 311.96 versus 1,905.71), mean error rate (0.14 versus 0.15 and 0.11 versus 0.82), and root mean square percentage error (0.26 versus 0.26 and 0.24 versus 1.01). Autoregressive fractionally integrated moving average predicted 181,650 (95% CI: 46,518-316,783) HC cases, averaging 22,706 (95% CI: 5,815-39,598) cases annually during 2023-2030. Henan faces challenges in eliminating HC epidemics, emphasizing the need for strengthened strategies. Autoregressive fractionally integrated moving average can offer evidence-based insights for public health measures.
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Affiliation(s)
- Yongbin Wang
- Department of Epidemiology and Health Statistics, School of Public Health, The First Affiliated Hospital, Xinxiang Medical University, Xinxiang, People’s Republic of China
| | - Ziyue Liang
- Department of Epidemiology and Health Statistics, School of Public Health, The First Affiliated Hospital, Xinxiang Medical University, Xinxiang, People’s Republic of China
| | - Siyu Qing
- Department of Epidemiology and Health Statistics, School of Public Health, The First Affiliated Hospital, Xinxiang Medical University, Xinxiang, People’s Republic of China
| | - Xingyan Liu
- Department of Epidemiology and Health Statistics, School of Public Health, The First Affiliated Hospital, Xinxiang Medical University, Xinxiang, People’s Republic of China
| | - Chunjie Xu
- Beijing Key Laboratory of Antimicrobial Agents/Laboratory of Pharmacology, Institute of Medicinal Biotechnology, Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing, Republic of China
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3
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Anand M, Danumjaya P, Rao PRS. A nonlinear mathematical model on the Covid-19 transmission pattern among diabetic and non-diabetic population. MATHEMATICS AND COMPUTERS IN SIMULATION 2023; 210:346-369. [PMID: 36994146 PMCID: PMC10027672 DOI: 10.1016/j.matcom.2023.03.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 02/14/2023] [Accepted: 03/14/2023] [Indexed: 06/19/2023]
Abstract
In this paper, a three tier mathematical model describing the interactions between susceptible population, Covid-19 infected, diabetic population and Covid-19 infected, non diabetic population is proposed. Basic properties of such a dynamic model, namely, non negativity, boundedness of solutions, existence of disease-free and disease equilibria are studied and sufficient conditions are obtained. Basic reproduction number for the system is derived. Sufficient conditions on functionals and parameters of the system are obtained for the local as well as global stability of equilibria, thus, establishing the conditions for eventual prevalence of disease free or disease environment, as the case may be. The stability aspects are discussed in the context of basic reproduction number and vice versa. An important contribution of this article is that a novel technique is presented to estimate some key, influencing parameters of the system so that a pre-specified, assumed equilibrium state is approached eventually. This enables the society to prepare itself with the help of these key, influencing parameters so estimated. Several examples are provided to illustrate the results established and simulations are provided to visualize the examples.
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Affiliation(s)
- Monalisa Anand
- Department of Mathematics, BITS-Pilani KK Birla Goa Campus, Goa 403726, India
| | - P Danumjaya
- Department of Mathematics, BITS-Pilani KK Birla Goa Campus, Goa 403726, India
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Rakhshan SA, Nejad MS, Zaj M, Ghane FH. Global analysis and prediction scenario of infectious outbreaks by recurrent dynamic model and machine learning models: A case study on COVID-19. Comput Biol Med 2023; 158:106817. [PMID: 36989749 PMCID: PMC10035804 DOI: 10.1016/j.compbiomed.2023.106817] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 03/10/2023] [Accepted: 03/20/2023] [Indexed: 03/25/2023]
Abstract
It is essential to evaluate patient outcomes at an early stage when dealing with a pandemic to provide optimal clinical care and resource management. Many methods have been proposed to provide a roadmap against different pandemics, including the recent pandemic disease COVID-19. Due to recurrent epidemic waves of COVID-19, which have been observed in many countries, mathematical modeling and forecasting of COVID-19 are still necessary as long as the world continues to battle against the pandemic. Modeling may aid in determining which interventions to try or predict future growth patterns. In this article, we design a combined approach for analyzing any pandemic in two separate parts. In the first part of the paper, we develop a recurrent SEIRS compartmental model to predict recurrent outbreak patterns of diseases. Due to its time-varying parameters, our model is able to reflect the dynamics of infectious diseases, and to measure the effectiveness of the restrictive measures. We discuss the stable solutions of the corresponding autonomous system with frozen parameters. We focus on the regime shifts and tipping points; then we investigate tipping phenomena due to parameter drifts in our time-varying parameters model that exhibits a bifurcation in the frozen-in case. Furthermore, we propose an optimal numerical design for estimating the system’s parameters. In the second part, we introduce machine learning models to strengthen the methodology of our paper in data analysis, particularly for prediction scenarios. We use MLP, RBF, LSTM, ANFIS, and GRNN for training and evaluation of COVID-19. Then, we compare the results with the recurrent dynamical system in the fitting process and prediction scenario. We also confirm results by implementing our methods on the released data on COVID-19 by WHO for Italy, Germany, Iran, and South Africa between 1/22/2020 and 7/24/2021, when people were engaged with different variants including Alpha, Beta, Gamma, and Delta. The results of this article show that the dynamic model is adequate for long-term analysis and data fitting, as well as obtaining parameters affecting the epidemic. However, it is ineffective in providing a long-term forecast. In contrast machine learning methods effectively provide disease prediction, although they do not provide analysis such as dynamic models. Finally, some metrics, including RMSE, R-Squared, and accuracy, are used to evaluate the machine learning models. These metrics confirm that ANFIS and RBF perform better than other methods in training and testing zones.
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Affiliation(s)
| | - Mahdi Soltani Nejad
- Department of Railway Engineering, Iran University of Science and Technology, Iran
| | - Marzie Zaj
- Department of Mathematics, Ferdowsi University of Mashhad, Iran
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5
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Kubra KT, Ali R. Modeling and analysis of novel COVID-19 outbreak under fractal-fractional derivative in Caputo sense with power-law: a case study of Pakistan. MODELING EARTH SYSTEMS AND ENVIRONMENT 2023; 9:1-18. [PMID: 37361699 PMCID: PMC10019432 DOI: 10.1007/s40808-023-01747-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 02/11/2023] [Indexed: 03/18/2023]
Abstract
In this paper, a five-compartment model is used to explore the dynamics of the COVID-19 pandemic, taking the vaccination campaign into account. The present model consists of five components that lead to a system of five ordinary differential equations. In this paper, we examined the disease from the perspective of a fractal fractional derivative in the Caputo sense with a power law type kernal. The model is also fitted with real data for Pakistan between June 1, 2020, and March 8, 2021. The fundamental mathematical characteristics of the model have been investigated thoroughly. We have calculated the equilibrium points and the reproduction number for the model and obtained the feasible region for the system. The existence and stability criteria of the model have been validated using the Banach fixed point theory and the Picard successive approximation technique. Furthermore, we have conducted stability analysis for both the disease-free and endemic equilibrium states. On the basis of sensitivity analysis and the dynamics of the threshold parameter, we have estimated the effectiveness of vaccination and identified potential control strategies for the disease using the proposed model outbreaks. The stability of the concerned solution in Ulam-Hyers and Ulam-Hyers-Rassias sense is also investigated. For the proposed problem, some results regarding basic reproduction numbers and stability analysis for various parameters are represented graphically. Matlab software is used for numerical illustrations. Graphical representations are given for different fractional orders and for various parametric values.
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Affiliation(s)
- Khadija Tul Kubra
- Department of Mathematics, Government College University Faisalabad, Faisalabad, 38000 Pakistan
| | - Rooh Ali
- Department of Mathematics, Government College University Faisalabad, Faisalabad, 38000 Pakistan
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6
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Shakhmurov VB, Kurulay M, Sahmurova A, Gursesli MC, Lanata A. Interaction of Virus in Cancer Patients: A Theoretical Dynamic Model. Bioengineering (Basel) 2023; 10:224. [PMID: 36829718 PMCID: PMC9952378 DOI: 10.3390/bioengineering10020224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2023] [Revised: 01/30/2023] [Accepted: 02/01/2023] [Indexed: 02/11/2023] Open
Abstract
This study reports on a phase-space analysis of a mathematical model of tumor growth with the interaction between virus and immune response. In this study, a mathematical determination was attempted to demonstrate the relationship between uninfected cells, infected cells, effector immune cells, and free viruses using a dynamic model. We revealed the stability analysis of the system and the Lyapunov stability of the equilibrium points. Moreover, all endemic equilibrium point models are derived. We investigated the stability behavior and the range of attraction sets of the nonlinear systems concerning our model. Furthermore, a global stability analysis is proved either in the construction of a Lyapunov function showing the validity of the concerned disease-free equilibria or in endemic equilibria discussed by the model. Finally, a simulated solution is achieved and the relationship between cancer cells and other cells is drawn.
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Affiliation(s)
- Veli B. Shakhmurov
- Department of Industrial Engineering, Antalya Bilim University, Ciplakli Mahallesi Farabi Caddesi 23 Dosemealti, Antalya 07190, Turkey
- Center of Analytical-Information Resource, Azerbaijan State Economic University, 194 M. Mukhtarov, Baku AZ1001, Azerbaijan
| | - Muhammet Kurulay
- Department of Mathematics Engineering, Yildiz Technical University, Istanbul 34225, Turkey
| | - Aida Sahmurova
- Department of Nursing, Antalya Bilim University, Ciplakli Mahallesi Farabi Caddesi 23 Dosemealti, Antalya 07190, Turkey
| | - Mustafa Can Gursesli
- Department of Information Engineering, University of Florence, Via Santa Marta 3, 50139 Firenze, Italy
- Department of Education, Literatures, Intercultural Studies, Languages and Psychology, University of Florence, 50135 Florence, Italy
| | - Antonio Lanata
- Department of Information Engineering, University of Florence, Via Santa Marta 3, 50139 Firenze, Italy
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Chen BL, Yuan B, Jiang WX, Yu YT, Ji M. Research on epidemic spread model based on cold chain input. Soft comput 2023; 27:2251-2268. [PMID: 36694866 PMCID: PMC9851120 DOI: 10.1007/s00500-023-07823-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/05/2023] [Indexed: 01/20/2023]
Abstract
In recent years, the new type of coronary pneumonia (COVID-19) has become a highly contagious disease worldwide, posing a serious threat to the public health. This paper is based on the SEIR model of the new coronavirus pneumonia, considering the impact of cold chain input and re-positive on the spread of the virus in the COVID-19. In the process of model design, the food cold chain and re-positive are used as parameters, and its stability is analyzed and simulated. The experimental results show that taking into account the cold chain input and re-positive can effectively simulate the spread of the epidemic. The research results have important research value and practical significance for the prevention and control of the COVID-19 and the prediction of important time nodes.
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Affiliation(s)
- Bo-Lun Chen
- Department of Computer Science, Huaiyin Institute of Technology, Huaiyin, 223003 Jiangsu China ,Institute of Informatics, University of Zurich, 8050 Zurich, Switzerland
| | - Ben Yuan
- Department of Computer Science, Huaiyin Institute of Technology, Huaiyin, 223003 Jiangsu China
| | - Win-Xin Jiang
- Department of Computer Science, Huaiyin Institute of Technology, Huaiyin, 223003 Jiangsu China
| | - Yong-Tao Yu
- Department of Computer Science, Huaiyin Institute of Technology, Huaiyin, 223003 Jiangsu China
| | - Min Ji
- Department of Computer Science, Huaiyin Institute of Technology, Huaiyin, 223003 Jiangsu China
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A robust study of a piecewise fractional order COVID-19 mathematical model. ALEXANDRIA ENGINEERING JOURNAL 2022; 61. [PMCID: PMC8604677 DOI: 10.1016/j.aej.2021.11.039] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
In the current manuscript, we deal with the dynamics of a piecewise covid-19 mathematical model with quarantine class and vaccination using SEIQR epidemic model. For this, we discussed the deterministic, stochastic, and fractional forms of the proposed model for different steps. It has a great impact on the infectious disease models and especially for covid-19 because in start the deterministic model played its role but with time due to uncertainty the stochastic model takes place and with long term expansion the use of fractional derivatives are required. The stability of the model is discussed regarding the reproductive number. Using the non-standard finite difference scheme for the numerical solution of the deterministic model and illustrate the obtained results graphically. Further, environmental noises are added to the model for the description of the stochastic model. Then take out the existence and uniqueness of positive solution with extinction for infection. Finally, we utilize a new technique of piecewise differential and integral operators for approximating Caputo-Fabrizio fractional derivative operator for the purpose of constructing of the fractional-order model. Then study the dynamics of the models such as positivity and boundedness of the solutions and local stability analysis. Solved numerically fractional-order model used Newton Polynomial scheme and present the results graphically.
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9
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Algarni AD, Ben Hamed A, Hamdi M, Elmannai H, Meshoul S. Mathematical COVID-19 model with vaccination: a case study in Saudi Arabia. PeerJ Comput Sci 2022; 8:e959. [PMID: 35634103 PMCID: PMC9137965 DOI: 10.7717/peerj-cs.959] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Accepted: 04/04/2022] [Indexed: 06/15/2023]
Abstract
The discovery of a new form of corona-viruses in December 2019, SARS-CoV-2, commonly named COVID-19, has reshaped the world. With health and economic issues at stake, scientists have been focusing on understanding the dynamics of the disease, in order to provide the governments with the best policies and strategies allowing them to reduce the span of the virus. The world has been waiting for the vaccine for more than one year. The World Health Organization (WHO) is advertising the vaccine as a safe and effective measure to fight off the virus. Saudi Arabia was the fourth country in the world to start to vaccinate its population. Even with the new simplified COVID-19 rules, the third dose is still mandatory. COVID-19 vaccines have raised many questions regarding in its efficiency and its role to reduce the number of infections. In this work, we try to answer these question and propose a new mathematical model with five compartments, including susceptible, vaccinated, infectious, asymptotic and recovered individuals. We provide theoretical results regarding the effective reproduction number, the stability of endemic equilibrium and disease free equilibrium. We provide numerical analysis of the model based on the Saudi case. Our developed model shows that the vaccine reduces the transmission rate and provides an explanation to the rise in the number of new infections immediately after the start of the vaccination campaign in Saudi Arabia.
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Affiliation(s)
- Abeer D. Algarni
- Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
| | | | - Monia Hamdi
- Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
| | - Hela Elmannai
- Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
| | - Souham Meshoul
- Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
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Harjule P, Poonia RC, Agrawal B, Saudagar AKJ, Altameem A, Alkhathami M, Khan MB, Hasanat MHA, Malik KM. An Effective Strategy and Mathematical Model to Predict the Sustainable Evolution of the Impact of the Pandemic Lockdown. Healthcare (Basel) 2022; 10:759. [PMID: 35627896 PMCID: PMC9141252 DOI: 10.3390/healthcare10050759] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2022] [Revised: 04/02/2022] [Accepted: 04/04/2022] [Indexed: 12/04/2022] Open
Abstract
There have been considerable losses in terms of human and economic resources due to the current coronavirus pandemic. This work, which contributes to the prevention and control of COVID-19, proposes a novel modified epidemiological model that predicts the epidemic's evolution over time in India. A mathematical model was proposed to analyze the spread of COVID-19 in India during the lockdowns implemented by the government of India during the first and second waves. What makes this study unique, however, is that it develops a conceptual model with time-dependent characteristics, which is peculiar to India's diverse and homogeneous societies. The results demonstrate that governmental control policies and suitable public perception of risk in terms of social distancing and public health safety measures are required to control the spread of COVID-19 in India. The results also show that India's two strict consecutive lockdowns (21 days and 19 days, respectively) successfully helped delay the spread of the disease, buying time to pump up healthcare capacities and management skills during the first wave of COVID-19 in India. In addition, the second wave's severe lockdown put a lot of pressure on the sustainability of many Indian cities. Therefore, the data show that timely implementation of government control laws combined with a high risk perception among the Indian population will help to ensure sustainability. The proposed model is an effective strategy for constructing healthy cities and sustainable societies in India, which will help prevent such a crisis in the future.
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Affiliation(s)
- Priyanka Harjule
- Department of Mathematics, Malaviya National Institute of Technology (MNIT), Jaipur 302017, India;
| | - Ramesh Chandra Poonia
- Department of Computer Science, CHRIST (Deemed to be University), Bangalore 560029, India;
| | - Basant Agrawal
- Department of Computer Science Engineering, Indian Institute of Information Technology Kota, MNIT Campus, Jaipur 302017, India;
| | - Abdul Khader Jilani Saudagar
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.A.); (M.A.); (M.B.K.); (M.H.A.H.)
| | - Abdullah Altameem
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.A.); (M.A.); (M.B.K.); (M.H.A.H.)
| | - Mohammed Alkhathami
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.A.); (M.A.); (M.B.K.); (M.H.A.H.)
| | - Muhammad Badruddin Khan
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.A.); (M.A.); (M.B.K.); (M.H.A.H.)
| | - Mozaherul Hoque Abul Hasanat
- Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.A.); (M.A.); (M.B.K.); (M.H.A.H.)
| | - Khalid Mahmood Malik
- Department of Computer Science and Engineering, Oakland University, Rochester, MI 48309, USA;
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Mathematical Modeling the Time-Delay Interactions between Tumor Viruses and the Immune System with the Effects of Chemotherapy and Autoimmune Diseases. MATHEMATICS 2022. [DOI: 10.3390/math10050756] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The immune system is the body’s defense against pathogens, which are complex living organisms found in many parts in the body including organs, tissues, cells, molecules, and proteins. When the immune system works properly, it can recognize and kill the abnormal cells and the infected cells. Otherwise, it can attack the body’s healthy cells even if there is no invader. Many researchers have developed immunotherapy (or cancer vaccines) and have used chemotherapy for cancer treatment that can kill fast-growing cancer cells or at least slow down tumor growth. However, chemotherapy drugs travel throughout the body and tend to kill both healthy cells and cancer cells. In this study, we consider the fact that chemotherapy can kill tumor cells and that the loss of the immune cells may at the same time stir up cancer growth. We present a dynamic time-delay tumor-immune model with the effects of chemotherapy drugs and autoimmune disease. The modeling results can be used to determine the progression of tumor cells in the human body with the effect of chemotherapy, autoimmune diseases, and time delays based on partial differential equations. It can also be used to predict when the tumor viruses’ free state can be reached as time progresses, as well as the state of the body’s healthy cells as time progresses. We also present a few numerical cases that illustrate that the model can be used to monitor the effects of chemotherapy drug treatment and the growth rate of tumor virus-infected cells and the autoimmune disease.
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Zeb A, Kumar P, Erturk VS, Sitthiwirattham T. A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms. JOURNAL OF KING SAUD UNIVERSITY. SCIENCE 2022; 34:101914. [PMID: 35194351 PMCID: PMC8851876 DOI: 10.1016/j.jksus.2022.101914] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 09/27/2021] [Accepted: 02/14/2022] [Indexed: 05/24/2023]
Abstract
The main purpose of this paper is to provide new vaccinated models of COVID-19 in the sense of Caputo-Fabrizio and new generalized Caputo-type fractional derivatives. The formulation of the given models is presented including an exhaustive study of the model dynamics such as positivity, boundedness of the solutions and local stability analysis. Furthermore, the unique solution existence for the proposed fractional order models is discussed via fixed point theory. Numerical solutions are also derived by using two-steps Adams-Bashforth algorithm for Caputo-Fabrizio operator, and modified Predictor-Corrector method for generalised Caputo fractional derivative. Our analysis allow to show that the given fractional-order models exemplify the dynamics of COVID-19 much better than the classical ones. Also, the analysis on the convergence and stability for the proposed methods are performed. By this study, we see that how the vaccine availability plays an important role in the control of COVID-19 infection.
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Affiliation(s)
- Anwar Zeb
- Department of Mathematics, COMSATS University Islamabad, Abbottabad 22060, K.P.K, Pakistan
| | - Pushpendra Kumar
- Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab, 151001, India
| | - Vedat Suat Erturk
- Department of Mathematics, Ondokuz Mayis University, Atakum-55200, Samsun, Turkey
| | - Thanin Sitthiwirattham
- Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
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Figueiredo CJJD, Mota CMDM, Rosa AGF, Souza APGD, Lima SMDS. Vulnerability to COVID-19 in Pernambuco, Brazil: A geospatial evaluation supported by multiple-criteria decision aid methodology. GEOSPATIAL HEALTH 2022; 17. [PMID: 35147014 DOI: 10.4081/gh.2022.1000] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Accepted: 07/08/2021] [Indexed: 06/14/2023]
Abstract
The paper presents an innovative application to identify areas vulnerable to coronavirus disease 2019 (COVID-19) considering a combination of spatial analysis and a multi-criteria learning approach. We applied this methodology in the state of Pernambuco, Brazil identifying vulnerable areas by considering a set of determinants and risk factors for COVID-19, including demographic, economic and spatial characteristics and the number of human COVID-19 infections. Examining possible patterns over a set number of days taking the number of cases recorded, we arrived at a set of compatible decision rules to explain the relation between risk factors and COVID-19 cases. The results reveal why certain municipalities are critically vulnerable to COVID-19 highlighting locations for which knowledge can be gained about environmental factors.
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Sinha AK, Namdev N, Shende P. Mathematical modeling of the outbreak of COVID-19. NETWORK MODELING AND ANALYSIS IN HEALTH INFORMATICS AND BIOINFORMATICS 2021; 11:5. [PMID: 34909367 PMCID: PMC8661390 DOI: 10.1007/s13721-021-00350-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Revised: 11/20/2021] [Accepted: 11/23/2021] [Indexed: 01/08/2023]
Abstract
The novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus's expanse have changed individuals' communication processes. Due to physical and financial factors, the population's density is more likely to interact and spread the virus. We establish a mathematical model to present the spread of the COVID-19 in India and worldwide. By the simulation process, we find the infected cases, infected fatality rate, and recovery rate of the COVID-19. We validate the model by the rough set method. In the method, we obtain the accuracy for the infected case is 90.19%, an infection-fatality of COVID-19 is 94%, and the recovery is 85.57%, approximately the same as the actual situation reported WHO. This paper uses the generalized simulation process to predict the outbreak of COVID-19 for different continents. It gives the way of future trends of the COVID-19 outbreak till December 2021 and casts enlightenment about learning the drifts of the outbreak worldwide.
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Affiliation(s)
- Arvind Kumar Sinha
- Department of Mathematics, National Institute of Technology Raipur, Raipur, Chhattisgarh 492010 India
| | - Nishant Namdev
- Department of Mathematics, National Institute of Technology Raipur, Raipur, Chhattisgarh 492010 India
| | - Pradeep Shende
- Department of Mathematics, National Institute of Technology Raipur, Raipur, Chhattisgarh 492010 India
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15
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Romano D, Stefanini C. Unveiling social distancing mechanisms via a fish-robot hybrid interaction. BIOLOGICAL CYBERNETICS 2021; 115:565-573. [PMID: 33730211 PMCID: PMC8960612 DOI: 10.1007/s00422-021-00867-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/19/2020] [Accepted: 02/20/2021] [Indexed: 06/12/2023]
Abstract
Pathogen transmission is a major limit of social species. Social distancing, a behavioural-based response to diseases, has been regularly reported in nature. However, the identification of distinctive stimuli associated with an infectious disease represents a challenging task for host species, whose cognitive mechanisms are still poorly understood. Herein, the social fish Paracheirodon innesi, was selected as model organism to investigate animal abilities in exploiting visual information to identify and promote social distancing towards potentially infected conspecifics. To address this, a robotic fish replica mimicking a healthy P. innesi subject, and another mimicking P. innesi with morphological and/or locomotion anomalies were developed. P. innesi individuals were attracted by the healthy fish replica, while they avoided the fish replica with morphological abnormalities, as well as the fish replica with an intact appearance, but performing locomotion anomalies (both symptoms associated with a microsporidian parasite infesting P. innesi and other fish). Furthermore, the fish replica presenting both morphology and locomotion anomalies in conjunction, triggered a significantly stronger social distancing response. This confirms the hypothesis that group living animals overgeneralize cues that can be related with a disease to minimize transmission, and highlights the important role of visual cues in infection risk contexts. This study prompts more attention on the role of behavioural-based strategies to avoid pathogen/parasite diffusion, and can be used to optimize computational approaches to model disease dynamics.
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Affiliation(s)
- Donato Romano
- The BioRobotics Institute, Sant'Anna School of Advanced Studies, Viale Rinaldo Piaggio 34, 56025, Pontedera, Pisa, Italy.
- Department of Excellence in Robotics and AI, Sant'Anna School of Advanced Studies, 56127, Pisa, Italy.
| | - Cesare Stefanini
- The BioRobotics Institute, Sant'Anna School of Advanced Studies, Viale Rinaldo Piaggio 34, 56025, Pontedera, Pisa, Italy
- Department of Excellence in Robotics and AI, Sant'Anna School of Advanced Studies, 56127, Pisa, Italy
- Healthcare Engineering Innovation Center (HEIC), Khalifa University, Abu Dhabi, UAE
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16
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Barrio RA, Kaski KK, Haraldsson GG, Aspelund T, Govezensky T. A model for social spreading of Covid-19: Cases of Mexico, Finland and Iceland. PHYSICA A 2021; 582:126274. [PMID: 34305295 PMCID: PMC8285360 DOI: 10.1016/j.physa.2021.126274] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/03/2020] [Revised: 07/08/2021] [Indexed: 06/13/2023]
Abstract
The shocking severity of the Covid-19 pandemic has woken up an unprecedented interest and accelerated effort of the scientific community to model and forecast epidemic spreading to find ways to control it regionally and between regions. Here we present a model that in addition to describing the dynamics of epidemic spreading with the traditional compartmental approach takes into account the social behaviour of the population distributed over a geographical region. The region to be modelled is defined as a two-dimensional grid of cells, in which each cell is weighted with the population density. In each cell a compartmental SEIRS system of delay difference equations is used to simulate the local dynamics of the disease. The infections between cells are modelled by a network of connections, which could be terrestrial, between neighbouring cells, or long range, between cities by air, road or train traffic. In addition, since people make trips without apparent reason, noise is considered to account for them to carry contagion between two randomly chosen distant cells. Hence, there is a clear separation of the parameters related to the biological characteristics of the disease from the ones that represent the spatial spread of infections due to social behaviour. We demonstrate that these parameters provide sufficient information to trace the evolution of the pandemic in different situations. In order to show the predictive power of this kind of approach we have chosen three, in a number of ways different countries, Mexico, Finland and Iceland, in which the pandemics have followed different dynamic paths. Furthermore we find that our model seems quite capable of reproducing the path of the pandemic for months with few initial data. Unlike similar models, our model shows the emergence of multiple waves in the case when the disease becomes endemic.
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Affiliation(s)
- Rafael A Barrio
- Instituto de Física, Universidad Nacional Autónoma de México, CDMX 01000, Mexico
| | - Kimmo K Kaski
- Department of Computer Science, Aalto University School of Science, Espoo, FI-00076, Finland
- The Alan Turing Institute, 96 Euston Rd, Kings Cross, London, NW1 2DB, UK
| | | | - Thor Aspelund
- Centre for Public Health Sciences, University of Iceland, Reykjavik, Iceland
- The Icelandic Heart Association, Reykjavik, Iceland
| | - Tzipe Govezensky
- Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, CDMX, 04510, Mexico
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17
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Hanthanan Arachchilage K, Hussaini MY. Ranking non-pharmaceutical interventions against Covid-19 global pandemic using global sensitivity analysis-Effect on number of deaths. CHAOS, SOLITONS, AND FRACTALS 2021; 152:111458. [PMID: 34580567 PMCID: PMC8457923 DOI: 10.1016/j.chaos.2021.111458] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Revised: 09/10/2021] [Accepted: 09/12/2021] [Indexed: 05/25/2023]
Abstract
In this study, we use Global Sensitivity Analysis (GSA) to rank four non-pharmaceutical interventions (NPIs) in a deterministic compartmental model that might control Covid-19 related deaths in the United States. The NPIs are social distancing, isolation of infected individuals, identifying asymptomatically infected individuals through testing, and the use of face masks. The model uses a fear-based behavioral model that leads unmasked susceptible individuals to wear masks. The model parameters are estimated from the reported deaths for the United States of America from March 1, 2020 to November 26, 2020. Two GSA tools, the Sobol' sesntivity indices and Partial Rank Correlation Coefficient are used to obtain the rankings of the input parameters at different stages of the disease propagation. We found that social distancing and outward mask efficiency alone decreases the output uncertainty by 25-45%. Sobol' second order indices show that the combined effect of social distancing with increased mask usage and identifying and isolating asymptomatically infected individuals decreases uncertainty an additional 10%.
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Affiliation(s)
| | - Mohammed Yousuff Hussaini
- Department of Mathematics, Florida State University, 1017, Academic Way, Tallahassee, 32304, Florida, USA
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18
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Wang Y, Xu C, Yao S, Wang L, Zhao Y, Ren J, Li Y. Estimating the COVID-19 prevalence and mortality using a novel data-driven hybrid model based on ensemble empirical mode decomposition. Sci Rep 2021; 11:21413. [PMID: 34725416 PMCID: PMC8560776 DOI: 10.1038/s41598-021-00948-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2020] [Accepted: 10/20/2021] [Indexed: 12/23/2022] Open
Abstract
In this study, we proposed a new data-driven hybrid technique by integrating an ensemble empirical mode decomposition (EEMD), an autoregressive integrated moving average (ARIMA), with a nonlinear autoregressive artificial neural network (NARANN), called the EEMD-ARIMA-NARANN model, to perform time series modeling and forecasting based on the COVID-19 prevalence and mortality data from 28 February 2020 to 27 June 2020 in South Africa and Nigeria. By comparing the accuracy level of forecasting measurements with the basic ARIMA and NARANN models, it was shown that this novel data-driven hybrid model did a better job of capturing the dynamic changing trends of the target data than the others used in this work. Our proposed mixture technique can be deemed as a helpful policy-supportive tool to plan and provide medical supplies effectively. The overall confirmed cases and deaths were estimated to reach around 176,570 [95% uncertainty level (UL) 173,607 to 178,476] and 3454 (95% UL 3384 to 3487), respectively, in South Africa, along with 32,136 (95% UL 31,568 to 32,641) and 788 (95% UL 775 to 804) in Nigeria on 12 July 2020 using this data-driven EEMD-ARIMA-NARANN hybrid technique. The contributions of this study include three aspects. First, the proposed hybrid model can better capture the dynamic dependency characteristics compared with the individual models. Second, this new data-driven hybrid model is constructed in a more reasonable way relative to the traditional mixture model. Third, this proposed model may be generalized to estimate the epidemic patterns of COVID-19 in other regions.
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Affiliation(s)
- Yongbin Wang
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, No. 601 Jinsui Road, Hongqi District, Xinxiang City, 453003, Henan Province, People's Republic of China.
| | - Chunjie Xu
- Department of Occupational and Environmental Health, School of Public Health, Capital Medical University, Beijing, People's Republic of China
| | - Sanqiao Yao
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, No. 601 Jinsui Road, Hongqi District, Xinxiang City, 453003, Henan Province, People's Republic of China
| | - Lei Wang
- Center for Musculoskeletal Surgery, Charité-Universitätsmedizin Berlin, Freie Universität Berlin, Humboldt-Universität zu Berlin and Berlin Institute of Health, Berlin, Germany
| | - Yingzheng Zhao
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, No. 601 Jinsui Road, Hongqi District, Xinxiang City, 453003, Henan Province, People's Republic of China
| | - Jingchao Ren
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, No. 601 Jinsui Road, Hongqi District, Xinxiang City, 453003, Henan Province, People's Republic of China
| | - Yuchun Li
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, No. 601 Jinsui Road, Hongqi District, Xinxiang City, 453003, Henan Province, People's Republic of China
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19
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Fotsa-Mbogne DJ, Tchoumi SY, Kouakep-Tchaptchie Y, Kamla VC, Kamgang JC, Houpa-Danga DE, Bowong-Tsakou S, Bekolle D. Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon. NONLINEAR DYNAMICS 2021; 106:2703-2738. [PMID: 34697521 PMCID: PMC8528969 DOI: 10.1007/s11071-021-06920-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 09/18/2021] [Indexed: 05/31/2023]
Abstract
This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). A multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism is proposed first. Indeed, there are human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self-infection by susceptible individuals. The global stability of the disease-free equilibrium is shown when a given threshold T 0 is less or equal to 1 and the basic reproduction number R 0 is calculated. A convergence index T 1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of infectious extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. Using Partial Rank Correlation Coefficient with a three levels fractional experimental design, the sensitivity of R 0 , T 0 and T 1 to control parameters is evaluated. Following this study, the most significant parameter is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into account economic impacts of SARS-CoV-2, optimal fighting strategies are determined and discussed. The study is applied to real and available data from Cameroon with a model fitting. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy against SARS-CoV-2.
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Affiliation(s)
- David Jaurès Fotsa-Mbogne
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Stéphane Yanick Tchoumi
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Yannick Kouakep-Tchaptchie
- Department of Fundamental Science and Engineering, EGCIM, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
| | - Vivient Corneille Kamla
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Jean-Claude Kamgang
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Duplex Elvis Houpa-Danga
- Department of Mathematics and Computer Science, FS, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
| | - Samuel Bowong-Tsakou
- Department of Mathematics and Computer Science, FS, The University of Douala, P.O. Box 24157, Douala, Cameroon
| | - David Bekolle
- Department of Mathematics and Computer Science, FS, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
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20
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A Dynamic Model of Multiple Time-Delay Interactions between the Virus-Infected Cells and Body’s Immune System with Autoimmune Diseases. AXIOMS 2021. [DOI: 10.3390/axioms10030216] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
The immune system is a complex interconnected network consisting of many parts including organs, tissues, cells, molecules and proteins that work together to protect the body from illness when germs enter the body. An autoimmune disease is a disease in which the body’s immune system attacks healthy cells. It is known that when the immune system is working properly, it can clearly recognize and kill the abnormal cells and virus-infected cells. But when it doesn’t work properly, the human body will not be able to recognize the virus-infected cells and, therefore, it can attack the body’s healthy cells when there is no invader or does not stop an attack after the invader has been killed, resulting in autoimmune disease.; This paper presents a mathematical modeling of the virus-infected development in the body’s immune system considering the multiple time-delay interactions between the immune cells and virus-infected cells with autoimmune disease. The proposed model aims to determine the dynamic progression of virus-infected cell growth in the immune system. The patterns of how the virus-infected cells spread and the development of the body’s immune cells with respect to time delays will be derived in the form of a system of delay partial differential equations. The model can be used to determine whether the virus-infected free state can be reached or not as time progresses. It also can be used to predict the number of the body’s immune cells at any given time. Several numerical examples are discussed to illustrate the proposed model. The model can provide a real understanding of the transmission dynamics and other significant factors of the virus-infected disease and the body’s immune system subject to the time delay, including approaches to reduce the growth rate of virus-infected cell and the autoimmune disease as well as to enhance the immune effector cells.
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21
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Afzal A, Saleel CA, Bhattacharyya S, Satish N, Samuel OD, Badruddin IA. Merits and Limitations of Mathematical Modeling and Computational Simulations in Mitigation of COVID-19 Pandemic: A Comprehensive Review. ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING : STATE OF THE ART REVIEWS 2021; 29:1311-1337. [PMID: 34393475 PMCID: PMC8356220 DOI: 10.1007/s11831-021-09634-2] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/22/2020] [Accepted: 07/04/2021] [Indexed: 06/13/2023]
Abstract
Mathematical models have assisted in describing the transmission and propagation dynamics of various viral diseases like MERS, measles, SARS, and Influenza; while the advanced computational technique is utilized in the epidemiology of viral diseases to examine and estimate the influences of interventions and vaccinations. In March 2020, the World Health Organization (WHO) has declared the COVID-19 as a global pandemic and the rate of morbidity and mortality triggers unprecedented public health crises throughout the world. The mathematical models can assist in improving the interventions, key transmission parameters, public health agencies, and countermeasures to mitigate this pandemic. Besides, the mathematical models were also used to examine the characteristics of epidemiological and the understanding of the complex transmission mechanism. Our literature study found that there were still some challenges in mathematical modeling for the case of ecology, genetics, microbiology, and pathology pose; also, some aspects like political and societal issues and cultural and ethical standards are hard to be characterized. Here, the recent mathematical models about COVID-19 and their prominent features, applications, limitations, and future perspective are discussed and reviewed. This review can assist in further improvement of mathematical models that will consider the current challenges of viral diseases.
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Affiliation(s)
- Asif Afzal
- Department of Mechanical Engineering, P. A. College of Engineering (Affiliated to Visvesvaraya Technological University, Belagavi), Mangaluru, India
| | - C. Ahamed Saleel
- Department of Mechanical Engineering, College of Engineering, King Khalid University, PO Box 394, Abha, 61421 Kingdom of Saudi Arabia
| | - Suvanjan Bhattacharyya
- Department of Mechanical Engineering, Birla Institute of Technology and Science Pilani, Pilani Campus, Vidhya Vihar, Rajasthan 333031 India
| | - N. Satish
- Department of Mechanical Engineering, DIET, Vijayawada, India
| | - Olusegun David Samuel
- Department of Mechanical Engineering, Federal University of Petroleum Resources, PMB 1221, Effurun, Delta State Nigeria
- Department of Mechanical Engineering, University of South Africa, Science Campus, Private Bag X6, Florida, 1709 South Africa
| | - Irfan Anjum Badruddin
- Department of Mechanical Engineering, College of Engineering, King Khalid University, PO Box 394, Abha, 61421 Kingdom of Saudi Arabia
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22
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Linear parameter varying model of COVID-19 pandemic exploiting basis functions. Biomed Signal Process Control 2021; 70:102999. [PMID: 34306169 PMCID: PMC8292062 DOI: 10.1016/j.bspc.2021.102999] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2021] [Revised: 06/07/2021] [Accepted: 07/17/2021] [Indexed: 12/23/2022]
Abstract
Current outbreaks of the COIVD-19 pandemic demonstrate a global threat. In this paper, a conceptual model is developed for the COVID-19 pandemic, in which the people in society are divided into Susceptible, Exposed, Minor infected (Those who need to be quarantined at home), Hospitalized (Those who are in need of hospitalization), Intensive infected (ventilator-in-need infected), Recovered and Deceased. In this paper, first, the model that is briefly called SEMHIRD for a sample country (Italy as an example) is considered. Then, exploiting the real data of the country, the parameters of the model are obtained by assuming some basis functions on the collected data and solving linear least square problems in each window of data to estimate the time-varying parameters of the model. Thus, the parameters are updated every few days, and the system behavior is modeled according to the changes in the parameters. Then, the Linear Parameter Varying (LPV) Model of COVID19 is derived, and its stability analysis is presented. In the end, the influence of different levels of social distancing and quarantine on the variation of severely infected and hospitalized people is studied.
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23
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Gandzha IS, Kliushnichenko OV, Lukyanets SP. Modeling and controlling the spread of epidemic with various social and economic scenarios. CHAOS, SOLITONS, AND FRACTALS 2021; 148:111046. [PMID: 34103789 PMCID: PMC8174143 DOI: 10.1016/j.chaos.2021.111046] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 05/06/2021] [Indexed: 06/12/2023]
Abstract
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe various scenarios of epidemic spreading. As compared to the basic SIR model, our model takes into account two possible routes of contagion transmission: direct from the infected compartment to the susceptible compartment and indirect via some intermediate medium or fomites. Transmission rates are estimated in terms of average distances between the individuals in selected social environments and characteristic time spans for which the individuals stay in each of these environments. We also introduce a collective economic resource associated with the average amount of money or income per individual to describe the socioeconomic interplay between the spreading process and the resource available to infected individuals. The epidemic-resource coupling is supposed to be of activation type, with the recovery rate governed by the Arrhenius-like law. Our model brings an advantage of building various control strategies to mitigate the effect of epidemic and can be applied, in particular, to modeling the spread of COVID-19.
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Affiliation(s)
- I S Gandzha
- Institute of Physics, National Academy of Sciences of Ukraine, Prosp. Nauky 46, Kyiv 03028, Ukraine
| | - O V Kliushnichenko
- Institute of Physics, National Academy of Sciences of Ukraine, Prosp. Nauky 46, Kyiv 03028, Ukraine
| | - S P Lukyanets
- Institute of Physics, National Academy of Sciences of Ukraine, Prosp. Nauky 46, Kyiv 03028, Ukraine
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24
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Ullah A, Ahmad S, Rahman GU, Alqarni MM, Mahmoud EE. Impact of pangolin bootleg market on the dynamics of COVID-19 model. RESULTS IN PHYSICS 2021; 23:103913. [PMID: 33623730 PMCID: PMC7892304 DOI: 10.1016/j.rinp.2021.103913] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2020] [Revised: 01/27/2021] [Accepted: 01/28/2021] [Indexed: 06/12/2023]
Abstract
In this paper we consider ant-eating pangolin as a possible source of the novel corona virus (COVID-19) and propose a new mathematical model describing the dynamics of COVID-19 pandemic. Our new model is based on the hypotheses that the pangolin and human populations are divided into measurable partitions and also incorporates pangolin bootleg market or reservoir. First we study the important mathematical properties like existence, boundedness and positivity of solution of the proposed model. After finding the threshold quantity for the underlying model, the possible stationary states are explored. We exploit linearization as well as Lyapanuv function theory to exhibit local stability analysis of the model in terms of the threshold quantity. We then discuss the global stability analyses of the newly introduced model and found conditions for its stability in terms of the basic reproduction number. It is also shown that for certain values of R 0 , our model exhibits a backward bifurcation. Numerical simulations are performed to verify and support our analytical findings.
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Affiliation(s)
- Abd Ullah
- Department of Mathematics, University of Malakand Chakdara, Dir (L), Pakhtunkhwa, Pakistan
| | - Saeed Ahmad
- Department of Mathematics, University of Malakand Chakdara, Dir (L), Pakhtunkhwa, Pakistan
| | - Ghaus Ur Rahman
- Department of Mathematics and Statistics, University of Swat, District Swat, Pakistan
| | - M M Alqarni
- Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
| | - Emad E Mahmoud
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
- Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
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25
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Abstract
In this paper, we applied the Sobol’s method on an already existing mathematical model of coronavirus disease 2019 (covid-19). The objectives of this research work are to study the individual effects of involved parameters as well as combine (mutual) effects of parameters on output variables of covid-19 model. The study is also useful to identify the ranking of key model parameters and factors fixing. The ultimate goal is to identify the controlling parameters, which eventually will help decision makers to explore various policy options to control the covid-19 pandemic. For this purpose, first we present the model with its basic properties that are positivity and existence of solution. Then use the Sobol’s method to discuss the individual effects of involved parameters as well as combine (mutual) effects of parameters on output variables of covid-19 model. Finally, we present the results, discussions and concluding remarks about key model parameters and identifying the controlling parameters, which eventually will help decision makers to explore various policy options to control the covid-19 pandemic.
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26
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Mahmoud NM, Mahmoud MH, Alamery S, Fouad H. Structural modeling and phylogenetic analysis for infectious disease transmission pattern based on maximum likelihood tree approach. JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2021; 12:3479-3492. [PMID: 33425052 PMCID: PMC7778505 DOI: 10.1007/s12652-020-02702-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2020] [Accepted: 11/16/2020] [Indexed: 06/12/2023]
Abstract
The contagious disease transmission pattern outbreak caused a massive human casualty and became a pandemic, as confirmed by the World Health Organization (WHO). The present research aims to understand the infectious disease transmission pattern outbreak due to molecular epidemiology. Hence, infected patients over time can spread infectious disease. The virus may develop further mutations, and that there might be a more toxic virulent strain, which leads to several environmental risk factors. Therefore, it is essential to monitor and characterize patient profiles, variants, symptoms, geographic locations, and treatment responses to analyze and evaluate infectious disease patterns among humans. This research proposes the Evolutionary tree analysis (ETA) for the molecular evolutionary genetic analysis to reduce medical risk factors. Furthermore, The Maximum likelihood tree method (MLTM) has been used to analyze the selective pressure, which is examined to identify a mutation that may influence the infectious disease transmission pattern's clinical progress. This study also utilizes ETA with Markov Chain Bayesian Statistics (MCBS) approach to reconstruct transmission trees with sequence information. The experimental shows that the proposed ETA-MCBS method achieves a 97.55% accuracy, prediction of 99.56%, and 98.55% performance compared to other existing methods.
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Affiliation(s)
- Nourelhoda M. Mahmoud
- Biomedical Engineering Department, Faculty of Engineering, Minia University, Minia, Egypt
| | - Mohamed H. Mahmoud
- Department of Biochemistry, College of Science, King Saud University, PO Box 22452, Riyadh, 11451 Saudi Arabia
| | - Salman Alamery
- Department of Biochemistry, College of Science, King Saud University, PO Box 22452, Riyadh, 11451 Saudi Arabia
| | - Hassan Fouad
- Biomedical Engineering Department, Faculty of Engineering, Helwan University, Cairo, Egypt
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27
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Logeswari K, Ravichandran C, Nisar KS. Mathematical model for spreading of COVID-19 virus with the Mittag-Leffler kernel. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2020; 40:NUM22652. [PMID: 33362342 PMCID: PMC7753447 DOI: 10.1002/num.22652] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2020] [Revised: 10/09/2020] [Accepted: 10/21/2020] [Indexed: 05/20/2023]
Abstract
In the Nidovirales order of the Coronaviridae family, where the coronavirus (crown-like spikes on the surface of the virus) causing severe infections like acute lung injury and acute respiratory distress syndrome. The contagion of this virus categorized as severed, which even causes severe damages to human life to harmless such as a common cold. In this manuscript, we discussed the SARS-CoV-2 virus into a system of equations to examine the existence and uniqueness results with the Atangana-Baleanu derivative by using a fixed-point method. Later, we designed a system where we generate numerical results to predict the outcome of virus spreadings all over India.
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Affiliation(s)
- Kumararaju Logeswari
- Postgraduate and Research Department of MathematicsKongunadu Arts and Science College(Autonomous)CoimbatoreTamil NaduIndia
| | - Chokkalingam Ravichandran
- Postgraduate and Research Department of MathematicsKongunadu Arts and Science College(Autonomous)CoimbatoreTamil NaduIndia
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz UniversityWadi AldawaserSaudi Arabia
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28
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Matouk AE. Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance. CHAOS, SOLITONS, AND FRACTALS 2020; 140:110257. [PMID: 32904626 PMCID: PMC7456281 DOI: 10.1016/j.chaos.2020.110257] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Revised: 08/09/2020] [Accepted: 08/27/2020] [Indexed: 05/08/2023]
Abstract
Nowadays, exploring complex dynamic of epidemic models becomes a focal point for research after the outbreak of COVID-19 pandemic which has no vaccine or fully approved drug treatment up till now. Hence, complex dynamics in a susceptible-infected (SI) model for COVID-19 with multi-drug resistance (MDR) and its fractional-order counterpart are investigated. Existence of positive solution in fractional-order model is discussed. Local stability based on the fractional Routh-Hurwitz (FRH) conditions is considered. Also, new FRH conditions are introduced and proved for the fractional case (0,2]. All these FRH conditions are also applied to discuss local stability of the multi-drug resistance steady states. Chaotic attractors are also found in this model for both integer-order and fractional-order cases. Numerical tools such as Lyapunov exponents, Lyapunov spectrum and bifurcation diagrams are employed to confirm existence of these complex dynamics. This study helps to understand complex behaviors and predict spread of severe infectious diseases such as COVID-19.
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Affiliation(s)
- A E Matouk
- Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia
- College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia
- Mansoura Higher Institute for Engineering and Technology, Damietta High Way, Mansourah, Egypt
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29
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CBRR Model for Predicting the Dynamics of the COVID-19 Epidemic in Real Time. MATHEMATICS 2020. [DOI: 10.3390/math8101727] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Because of the lack of reliable information on the spread parameters of COVID-19, there is an increasing demand for new approaches to efficiently predict the dynamics of new virus spread under uncertainty. The study presented in this paper is based on the Case-Based Reasoning method used in statistical analysis, forecasting and decision making in the field of public health and epidemiology. A new mathematical Case-Based Rate Reasoning model (CBRR) has been built for the short-term forecasting of coronavirus spread dynamics under uncertainty. The model allows for predicting future values of the increase in the percentage of new cases for a period of 2–3 weeks. Information on the dynamics of the total number of infected people in previous periods in Italy, Spain, France, and the United Kingdom was used. Simulation results confirmed the possibility of using the proposed approach for constructing short-term forecasts of coronavirus spread dynamics. The main finding of this study is that using the proposed approach for Russia showed that the deviation of the predicted total number of confirmed cases from the actual one was within 0.3%. For the USA, the deviation was 0.23%.
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Forecasting the epidemiological trends of COVID-19 prevalence and mortality using the advanced α-Sutte Indicator. Epidemiol Infect 2020; 148:e236. [PMID: 33012300 PMCID: PMC7562786 DOI: 10.1017/s095026882000237x] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Forecasting the epidemics of the diseases is very valuable in planning and supplying resources effectively. This study aims to estimate the epidemiological trends of the coronavirus disease 2019 (COVID-19) prevalence and mortality using the advanced α-Sutte Indicator, and its prediction accuracy level was compared with the most frequently adopted autoregressive integrated moving average (ARIMA) method. Time-series analysis was performed based on the total confirmed cases and deaths of COVID-19 in the world, Brazil, Peru, Canada and Chile between 27 February 2020 and 30 June 2020. By comparing the prediction reliability indices, including the root mean square error, mean absolute error, mean error rate, mean absolute percentage error and root mean square percentage error, the α-Sutte Indicator was found to produce lower forecasting error rates than the ARIMA model in all data apart from the prevalence testing set globally. The α-Sutte Indicator can be recommended as a useful tool to nowcast and forecast the COVID-19 prevalence and mortality of these regions except for the prevalence around the globe in the near future, which will help policymakers to plan and prepare health resources effectively. Also, the findings of our study may have managerial implications for the outbreak in other countries.
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31
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Wang Y, Xu C, Yao S, Zhao Y, Li Y, Wang L, Zhao X. Estimating the Prevalence and Mortality of Coronavirus Disease 2019 (COVID-19) in the USA, the UK, Russia, and India. Infect Drug Resist 2020; 13:3335-3350. [PMID: 33061481 PMCID: PMC7532899 DOI: 10.2147/idr.s265292] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2020] [Accepted: 08/12/2020] [Indexed: 12/13/2022] Open
Abstract
Objective The aim of this study is to apply the advanced error-trend-seasonal (ETS) framework to forecast the prevalence and mortality series of COVID-19 in the USA, the UK, Russia, and India, and the predictive performance of the ETS framework was compared with the most frequently used autoregressive integrated moving average (ARIMA) model. Materials and Methods The prevalence and mortality data of COVID-19 in the USA, the UK, Russia, and India between 20 February 2020 and 15 May 2020 were extracted from the WHO website. Then, the data subsamples between 20 February 2020 and 3 May 2020 were treated as the training horizon, and the others were used as the testing horizon to construct the ARIMA models and the ETS models. Results Based on the model evaluation criteria, the ARIMA (0,2,1) and ETS (M,MD,N), sparse coefficient ARIMA (0,2,(1,6)) and ETS (A,AD,M), ARIMA (1,1,1) and ETS (A,MD,A), together with ARIMA (2,2,1) and ETS (A,M,A) specifications were identified as the preferred ARIMA and ETS models for the prevalence data in the USA, the UK, Russia, and India, respectively; the ARIMA (0,2,1) and ETS (M,A,M), ARIMA (0,2,1) and ETS (M,A,N), ARIMA (0,2,1) and ETS (A,A,N), coupled with ARIMA (0,2,2) and ETS (M,M,N) specifications were selected as the optimal ARIMA and ETS models for the mortality data in these four countries, respectively. Among these best-fitting models, the ETS models produced smaller forecasting error rates than the ARIMA models in all the datasets. Conclusion The ETS framework can be used to nowcast and forecast the long-term temporal trends of the COVID-19 prevalence and mortality in the USA, the UK, Russia, and India, and which provides a notable performance improvement over the most frequently used ARIMA model. Our findings can aid governments as a reference to prepare for and respond to the COVID-19 pandemic both in restricting the transmission of the disease and in lowering the disease-related deaths in the upcoming days.
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Affiliation(s)
- Yongbin Wang
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, People's Republic of China
| | - Chunjie Xu
- Department of Occupational and Environmental Health, School of Public Health, Capital Medical University, Beijing, People's Republic of China
| | - Sanqiao Yao
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, People's Republic of China
| | - Yingzheng Zhao
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, People's Republic of China
| | - Yuchun Li
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, People's Republic of China
| | - Lei Wang
- Center for Musculoskeletal Surgery, Charité Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin, Humboldt-Universität Zu Berlin and Berlin Institute of Health, Berlin, Germany
| | - Xiangmei Zhao
- Department of Epidemiology and Health Statistics, School of Public Health, Xinxiang Medical University, Xinxiang, Henan Province, People's Republic of China
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Haghani M, Bliemer MCJ. Covid-19 pandemic and the unprecedented mobilisation of scholarly efforts prompted by a health crisis: Scientometric comparisons across SARS, MERS and 2019-nCoV literature. Scientometrics 2020; 125:2695-2726. [PMID: 32981988 PMCID: PMC7505229 DOI: 10.1007/s11192-020-03706-z] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Accepted: 09/01/2020] [Indexed: 12/28/2022]
Abstract
During the current century, each major coronavirus outbreak has triggered a quick and immediate surge of academic publications on its respective topic. The spike in research publications following the 2019 Novel Coronavirus (Covid-19) outbreak, however, has been like no other. The global crisis caused by the Covid-19 pandemic has mobilised scientific efforts at an unprecedented scale. In less than 5 months, more than 12,000 research items and in less than seven months, more than 30,000 items were indexed, while it is projected that the number could exceed 80,000 by the end of 2020, should the current trend continues. With the health crisis affecting all aspects of life, research on Covid-19 seems to have become a focal point of interest across many academic disciplines. Here, scientometric aspects of the Covid-19 literature are analysed and contrasted with those of the two previous major coronavirus diseases, i.e., Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS). The focus is on the co-occurrence of key-terms, bibliographic coupling and citation relations of journals and collaborations between countries. Interesting recurring patterns across all three literatures were discovered. All three outbreaks have commonly generated three distinct cohorts of studies: (i) studies linked to public health response and epidemic control, (ii) studies on chemical constitution of the virus; and (iii) studies related to treatment, vaccine and clinical care. While studies affiliated with category (i) seem to have been relatively earliest to emerge, they have overall received relatively smaller number of citations compared to publications the two other categories. Covid-19 studies seem to have been disseminated across a broader variety of journals and across a more diverse range of subject areas. Clear links are observed between the geographical origins of each outbreak as well as the local geographical severity of each outbreak and the magnitude of research originated from regions. Covid-19 studies also display the involvement of authors from a broader variety of countries compared to SARS and MERS. Considering the speed at which the Covid-19-related literature is accumulating, an interesting dimension that warrants further exploration could be to assess if the quality and rigour of these publications have been affected.
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Affiliation(s)
- Milad Haghani
- Institute of Transport and Logistics Studies, The University of Sydney Business School, The University of Sydney, Sydney, NSW Australia
| | - Michiel C J Bliemer
- Institute of Transport and Logistics Studies, The University of Sydney Business School, The University of Sydney, Sydney, NSW Australia
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Mishra AM, Purohit SD, Owolabi KM, Sharma YD. A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus. CHAOS, SOLITONS, AND FRACTALS 2020; 138:109953. [PMID: 32565620 PMCID: PMC7269963 DOI: 10.1016/j.chaos.2020.109953] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Revised: 05/23/2020] [Accepted: 05/29/2020] [Indexed: 05/02/2023]
Abstract
In this article, we develop a mathematical model considering susceptible, exposed, infected, asymptotic, quarantine/isolation and recovered classes as in case of COVID-19 disease. The facility of quarantine/isolation have been provided to both exposed and infected classes. Asymptotic individuals either recovered without undergo treatment or moved to infected class after some duration. We have formulated the reproduction number for the proposed model. Elasticity and sensitivity analysis indicates that model is more sensitive towards the transmission rate from exposed to infected classes rather than transmission rate from susceptible to exposed class. Analysis of global stability for the proposed model is studied through Lyapunov's function.
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Affiliation(s)
- A M Mishra
- Department of Mathematics, Prof. Rajendra Singh (Rajju Bhaiya) Institute of Physical Sciences for Study and Research VBSPU Jaunpur 222003, India
- Department of HEAS (Mathematics), Rajasthan Technical University Kota 324010, India
| | - S D Purohit
- Department of HEAS (Mathematics), Rajasthan Technical University Kota 324010, India
| | - K M Owolabi
- Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
- Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria
| | - Y D Sharma
- Department of Mathematics, National Institute of Technology, Hamirpur 177001, India
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Zhang Z, Zeb A, Egbelowo OF, Erturk VS. Dynamics of a fractional order mathematical model for COVID-19 epidemic. ADVANCES IN DIFFERENCE EQUATIONS 2020; 2020:420. [PMID: 32834820 PMCID: PMC7427275 DOI: 10.1186/s13662-020-02873-w] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2020] [Accepted: 07/31/2020] [Indexed: 05/21/2023]
Abstract
In this work, we formulate and analyze a new mathematical model for COVID-19 epidemic with isolated class in fractional order. This model is described by a system of fractional-order differential equations model and includes five classes, namely, S (susceptible class), E (exposed class), I (infected class), Q (isolated class), and R (recovered class). Dynamics and numerical approximations for the proposed fractional-order model are studied. Firstly, positivity and boundedness of the model are established. Secondly, the basic reproduction number of the model is calculated by using the next generation matrix approach. Then, asymptotic stability of the model is investigated. Lastly, we apply the adaptive predictor-corrector algorithm and fourth-order Runge-Kutta (RK4) method to simulate the proposed model. Consequently, a set of numerical simulations are performed to support the validity of the theoretical results. The numerical simulations indicate that there is a good agreement between theoretical results and numerical ones.
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Affiliation(s)
- Zizhen Zhang
- School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu, 233030 China
| | - Anwar Zeb
- Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, 22060 Khyber Pakhtunkhwa Pakistan
| | - Oluwaseun Francis Egbelowo
- Division of Clinical Pharmacology, Department of Medicine, University of Cape Town, Cape Town, South Africa
| | - Vedat Suat Erturk
- Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mays University, 55139 Samsun, Turkey
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Tsikala Vafea M, Atalla E, Georgakas J, Shehadeh F, Mylona EK, Kalligeros M, Mylonakis E. Emerging Technologies for Use in the Study, Diagnosis, and Treatment of Patients with COVID-19. Cell Mol Bioeng 2020; 13:249-257. [PMID: 32837582 PMCID: PMC7314428 DOI: 10.1007/s12195-020-00629-w] [Citation(s) in RCA: 56] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2020] [Accepted: 06/18/2020] [Indexed: 12/23/2022] Open
Abstract
INTRODUCTION The COVID-19 pandemic has caused an unprecedented health and economic worldwide crisis. Innovative solutions are imperative given limited resources and immediate need for medical supplies, healthcare support and treatments. AIM The purpose of this review is to summarize emerging technologies being implemented in the study, diagnosis, and treatment of COVID-19. RESULTS Key focus areas include the applications of artificial intelligence, the use of Big Data and Internet of Things, the importance of mathematical modeling for predictions, utilization of technology for community screening, the use of nanotechnology for treatment and vaccine development, the utility of telemedicine, the implementation of 3D-printing to manage new demands and the potential of robotics. CONCLUSION The review concludes by highlighting the need for collaboration in the scientific community with open sharing of knowledge, tools, and expertise.
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Affiliation(s)
- Maria Tsikala Vafea
- Infectious Diseases Division, Rhode Island Hospital, Warren Alpert Medical School of Brown University, 593 Eddy Street, POB, 3rd Floor, Suite 328/330, Providence, RI 02903 USA
| | - Eleftheria Atalla
- Infectious Diseases Division, Rhode Island Hospital, Warren Alpert Medical School of Brown University, 593 Eddy Street, POB, 3rd Floor, Suite 328/330, Providence, RI 02903 USA
| | - Joanna Georgakas
- Infectious Diseases Division, Rhode Island Hospital, Warren Alpert Medical School of Brown University, 593 Eddy Street, POB, 3rd Floor, Suite 328/330, Providence, RI 02903 USA
| | - Fadi Shehadeh
- Infectious Diseases Division, Rhode Island Hospital, Warren Alpert Medical School of Brown University, 593 Eddy Street, POB, 3rd Floor, Suite 328/330, Providence, RI 02903 USA
| | - Evangelia K. Mylona
- Infectious Diseases Division, Rhode Island Hospital, Warren Alpert Medical School of Brown University, 593 Eddy Street, POB, 3rd Floor, Suite 328/330, Providence, RI 02903 USA
| | - Markos Kalligeros
- Infectious Diseases Division, Rhode Island Hospital, Warren Alpert Medical School of Brown University, 593 Eddy Street, POB, 3rd Floor, Suite 328/330, Providence, RI 02903 USA
| | - Eleftherios Mylonakis
- Infectious Diseases Division, Rhode Island Hospital, Warren Alpert Medical School of Brown University, 593 Eddy Street, POB, 3rd Floor, Suite 328/330, Providence, RI 02903 USA
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36
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Zhang Z, Zeb A, Alzahrani E, Iqbal S. Crowding effects on the dynamics of COVID-19 mathematical model. ADVANCES IN DIFFERENCE EQUATIONS 2020; 2020:675. [PMID: 33281894 PMCID: PMC7705858 DOI: 10.1186/s13662-020-03137-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2020] [Accepted: 11/23/2020] [Indexed: 05/21/2023]
Abstract
A disastrous coronavirus, which infects a normal person through droplets of infected person, has a route that is usually by mouth, eyes, nose or hands. These contact routes make it very dangerous as no one can get rid of it. The significant factor of increasing trend in COVID19 cases is the crowding factor, which we named "crowding effects". Modeling of this effect is highly necessary as it will help to predict the possible impact on the overall population. The nonlinear incidence rate is the best approach to modeling this effect. At the first step, the model is formulated by using a nonlinear incidence rate with inclusion of the crowding effect, then its positivity and proposed boundedness will be addressed leading to model dynamics using the reproductive number. Then to get the graphical results a nonstandard finite difference (NSFD) scheme and fourth order Runge-Kutta (RK4) method are applied.
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Affiliation(s)
- Zizhen Zhang
- School of Management Science and Engineering, University of Finance and Economics, Bengbu, 233030 China
| | - Anwar Zeb
- Department of Mathematics, COMSATS University Islamabad, Abbottabad, Pakistan
| | - Ebraheem Alzahrani
- Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia
| | - Sohail Iqbal
- Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan
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