1
|
Nisar KS, Farman M, Jamil K, Akgul A, Jamil S. Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator. PLoS One 2024; 19:e0298620. [PMID: 38625847 PMCID: PMC11021000 DOI: 10.1371/journal.pone.0298620] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2023] [Accepted: 01/27/2024] [Indexed: 04/18/2024] Open
Abstract
In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.
Collapse
Affiliation(s)
- Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser, Saudi Arabia
| | - Muhammad Farman
- Faculty of Arts and Sciences, Department of Mathematics, Near East University, Nicosia, Northern Cyprus, Turkey
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Khadija Jamil
- Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
| | - Ali Akgul
- Faculty of Arts and Science, Department of Mathematics, Siirt University, Siirt, Turkey
| | - Saba Jamil
- Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
| |
Collapse
|
2
|
Xue L, Sun Y, Ren X, Sun W. Modelling the transmission dynamics and optimal control strategies for HIV infection in China. JOURNAL OF BIOLOGICAL DYNAMICS 2023; 17:2174275. [PMID: 36787262 DOI: 10.1080/17513758.2023.2174275] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2022] [Accepted: 12/08/2022] [Indexed: 06/18/2023]
Abstract
In order to end the AIDS epidemic by 2030 that was put forward by the Joint United Nations Programme on HIV/AIDS in 2014, China needs to take more effective measures to achieve the three 90% goals (90-90-90). We establish a compartmental model to study the dynamics of HIV transmission with control strategies. The analytical results show the existence and stability of the disease-free equilibrium and endemic equilibrium. An optimal control model is constructed to evaluate the impacts of control measures. The simulation results show that the optimal control strategy proposed in this work can eradicate AIDS by 2030. The cost-effectiveness analysis indicates that the cost of the control strategy that combines screening for latent individuals and enhancing education for unaware infected individuals is the lowest. Our findings can provide guidance for public health authorities on effective mitigation strategies to achieve the goals proposed by the United Nations Program on HIV/AIDS.
Collapse
Affiliation(s)
- Ling Xue
- College of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of China
| | - Yuanmei Sun
- College of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of China
| | - Xue Ren
- College of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin, People's Republic of China
| | - Wei Sun
- College of Mathematical Sciences, Harbin Engineering University, Harbin, People's Republic of China
| |
Collapse
|
3
|
Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel. Symmetry (Basel) 2023. [DOI: 10.3390/sym15030665] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/09/2023] Open
Abstract
This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posedness and biological viability and disease free equilibrium points are confirmed. Many applications of fractional operators in modern mathematics exist, including the intricate and important study of symmetrical systems. Symmetry analysis is a powerful tool that enables the creation of numerical solutions for a given fractional differential equation very methodically. For this, we compare the results with the Caputo derivative operator to understand the dynamic behavior of the disease. The simulation demonstrates how all classes have convergent characteristics and maintain their places over time, reflecting the true behavior of Ebola virus infection. Power law kernel with the two step polynomial Newton method were used. This model seems to be quite strong and capable of reproducing the issue’s anticipated theoretical conditions.
Collapse
|
4
|
Melikechi O, Young AL, Tang T, Bowman T, Dunson D, Johndrow J. Limits of epidemic prediction using SIR models. J Math Biol 2022; 85:36. [PMID: 36125562 PMCID: PMC9487859 DOI: 10.1007/s00285-022-01804-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2021] [Revised: 08/12/2022] [Accepted: 08/30/2022] [Indexed: 11/27/2022]
Abstract
The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the model parameters based on noisy observations early in the outbreak, well before the epidemic reaches its peak. This allows prediction of the subsequent course of the epidemic and design of appropriate interventions. However, accurately inferring SIR model parameters in such scenarios is problematic. This article provides novel, theoretical insight on this issue of practical identifiability of the SIR model. Our theory provides new understanding of the inferential limits of routinely used epidemic models and provides a valuable addition to current simulate-and-check methods. We illustrate some practical implications through application to a real-world epidemic data set.
Collapse
Affiliation(s)
- Omar Melikechi
- Department of Mathematics, Duke University, Durham, NC, USA.
| | | | - Tao Tang
- Department of Mathematics, Duke University, Durham, NC, USA
| | - Trevor Bowman
- Department of Mathematics, Duke University, Durham, NC, USA
| | - David Dunson
- Department of Mathematics, Duke University, Durham, NC, USA.,Department of Statistics, Duke University, Durham, NC, USA
| | - James Johndrow
- Department of Statistics, University of Pennsylvania, Philadelphia, PA, USA
| |
Collapse
|
5
|
Ram D, Bhandari DS, Tripathi D, Sharma K. Propagation of H1N1 virus through saliva movement in oesophagus: a mathematical model. EUROPEAN PHYSICAL JOURNAL PLUS 2022; 137:866. [PMID: 35912042 PMCID: PMC9326416 DOI: 10.1140/epjp/s13360-022-03070-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/25/2022] [Accepted: 07/12/2022] [Indexed: 06/15/2023]
Abstract
H1N1 (Swine flu) is caused by the influenza A virus which belongs to the Orthomyxoviridae family. Influenza A is very harmful to the elderly, and people with chronic respiratory disease and cardiovascular disease. Therefore, it is essential to analyse the behaviour of virus transmission through the saliva movement in oesophagus. A mathematical paradigm is developed to study the saliva movement under the applications of transverse magnetic field. Jeffrey fluid model is considered for saliva to show the viscoelastic nature. The flow nature is considered creeping and assumptions of long wavelength and low Reynolds number are adopted for analytical solutions. The Basset-Boussinesq-Oseen equation is employed to understand the propagation of H1N1 virus through saliva under the effect of applicable forces such as gravity, virtual mass, basset force, and drag forces. The suitable data for saliva, oesophagus and H1N1 virus are taken from the existing literature for simulation of the results using MATLAB software. From the graphical results, it is observed that the susceptibility to viral infections is less because the magnetic field reduces the motion of the virus particle. Further, the chances of infections in males are more as compared to females and children due to variation in viscosity of saliva. Such findings provide an understanding of the mechanics of the virus floating through the saliva (viscoelastic fluids) in the oesophagus.
Collapse
Affiliation(s)
- Daya Ram
- Department of Mathematics, Malaviya National Institute of Technology Jaipur, Rajasthan, 302017 India
| | - D. S. Bhandari
- Department of Mathematics, National Institute of Technology, Uttarakhand, Srinagar, 246174 India
| | - Dharmendra Tripathi
- Department of Mathematics, National Institute of Technology, Uttarakhand, Srinagar, 246174 India
| | - Kushal Sharma
- Department of Mathematics, Malaviya National Institute of Technology Jaipur, Rajasthan, 302017 India
| |
Collapse
|
6
|
Serra M, Al-Mosleh S, Prasath G, Raju V, Mantena S, Chandra J, Iams S, Mahadevan L. Optimal policies for mitigating pandemic costs: a minimal model. Phys Biol 2022; 19. [PMID: 35790172 DOI: 10.1088/1478-3975/ac7e9e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2021] [Accepted: 07/05/2022] [Indexed: 11/11/2022]
Abstract
There have been a number of pharmaceutical and non-pharmaceutical interventions associated with COVID-19 over the past two years. Of the various non-pharmaceutical interventions that were proposed and implemented to control the spread of the COVID-19 pandemic partial and complete lockdowns were used repeatedly in an attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here, we use a minimal model to understand the costs and benefits of these strategies that mitigate pandemic costs subject to constraints, we adopt the language of optimal control theory. This allows us to determine top-down policies for the nature and dynamics of social contact rates given an age-structured model for the dynamics of the disease. Depending on the relative weights allocated to mortality and socioeconomic losses, we see that the optimal strategies range from long-term social-distancing only for the most vulnerable, to partial lockdown to ensure not over-running hospitals, to alternating-shifts with significant reduction in mortality and/or socioeconomic losses. Crucially, commonly used strategies that involve long periods of broad lockdown are almost never optimal, as they are highly unstable to reopening {and entail high socioeconomic costs}. Using parameter estimates from data available for Germany and the USA early in the pandemic, we quantify these policies and use sensitivity analysis in the relevant model parameters and initial conditions to determine the range of robustness of our policies. Finally we also discuss how bottom-up behavioral changes affect the dynamics of the pandemic and show they can work in tandem with top-down control policies to mitigate pandemic costs even more effectively.
Collapse
Affiliation(s)
- Mattia Serra
- Harvard University, Pierce Hall, Cambridge, Cambridge, 02138, UNITED STATES
| | - Salem Al-Mosleh
- School of Engineering and Applied Sciences, Harvard University, Pierce Hall, Cambridge, Cambridge, 02138, UNITED STATES
| | - Ganga Prasath
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford St, Cambridge, Cambridge, Massachusetts, 02138, UNITED STATES
| | - Vidya Raju
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford St, Cambridge, Cambridge, Massachusetts, 02138, UNITED STATES
| | - Sreekar Mantena
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford St, Cambridge, Cambridge, 02138, UNITED STATES
| | - Jay Chandra
- School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, 02138, UNITED STATES
| | - Sarah Iams
- Harvard University, 29 Oxford Street, Cambridge, 02138, UNITED STATES
| | - L Mahadevan
- Harvard University, 29 Oxford Street, Cambridge, Massachusetts, 02138, UNITED STATES
| |
Collapse
|
7
|
Modelling the Role of Human Behaviour in Ebola Virus Disease (EVD) Transmission Dynamics. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2022; 2022:4150043. [PMID: 35602345 PMCID: PMC9122724 DOI: 10.1155/2022/4150043] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Revised: 04/15/2022] [Accepted: 04/26/2022] [Indexed: 11/18/2022]
Abstract
The role of human behaviour in the dynamics of infectious diseases cannot be underestimated. A clear understanding of how human behaviour influences the spread of infectious diseases is critical in establishing and designing control measures. To study the role that human behaviour plays in Ebola disease dynamics, in this paper, we design an Ebola virus disease model with disease transmission dynamics based on a new exponential nonlinear incidence function. This new incidence function that captures the reduction in disease transmission due to human behaviour innovatively considers the efficacy and the speed of behaviour change. The model's steady states are determined and suitable Lyapunov functions are built. The proofs of the global stability of equilibrium points are presented. To demonstrate the utility of the model, we fit the model to Ebola virus disease data from Liberia and Sierra Leone. The results which are comparable to existing findings from the outbreak of 2014 − 2016 show a better fit when the efficacy and the speed of behaviour change are higher. A rapid and efficacious behaviour change as a control measure to rapidly control an Ebola virus disease epidemic is advocated. Consequently, this model has implications for the management and control of future Ebola virus disease outbreaks.
Collapse
|
8
|
Tadmon C, Kengne JN. Mathematical analysis of a model of Ebola disease with control measures. INT J BIOMATH 2022. [DOI: 10.1142/s1793524522500486] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The re-emergence of the Ebola virus disease has pushed researchers to investigate more on this highly deadly disease in order to better understand and control the outbreak and recurrence of epidemics. It is in this perspective that we formulate a realistic mathematical model for the dynamic transmission of Ebola virus disease, incorporating relevant control measures and factors such as ban on eating bush-meat, social distancing, observance of hygiene rules and containment, waning of the vaccine-induced, imperfect contact tracing and vaccine efficacy, quarantine, hospitalization and screening to fight against the spread of the disease. First, by considering the constant control parameters case, we thoroughly compute the control reproduction number [Formula: see text] from which the dynamics of the model is analyzed. The existence and stability of steady states are established under appropriate assumptions on [Formula: see text]. Also, the effect of all the control measures is investigated and the global sensitivity analysis of the control reproduction number is performed in order to determine the impact of parameters and their relative importance to disease transmission and prevalence. Second, in the time-dependent control parameters case, an optimal control problem is formulated to design optimal control strategies for eradicating the disease transmission. Using Pontryagin’s Maximum Principle, we derive necessary conditions for optimal control of the disease. The cost-effectiveness analysis of all combinations of the control measures is made by calculating the infection averted ratio and the incremental cost-effectiveness ratio. This reveals that combining the four restrictive measures conveyed through educational campaigns, screening, safe burial and the care of patients in health centers for better isolation is the most cost-effective among the strategies considered. Numerical simulations are performed to illustrate the theoretical results obtained.
Collapse
Affiliation(s)
- Calvin Tadmon
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67 Dschang, Cameroon
- The Abdus Salam International Centre for Theoretical, Physics Strada Costiera 11, 34151 Trieste, Italy
| | - Jacques Ndé Kengne
- Department of Mathematics and Computer Science, University of Dschang, P. O. Box 67 Dschang, Cameroon
| |
Collapse
|
9
|
Seck R, Ngom D, Ivorra B, Ramos ÁM. An optimal control model to design strategies for reducing the spread of the Ebola virus disease. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:1746-1774. [PMID: 35135227 DOI: 10.3934/mbe.2022082] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this work, we formulate an epidemiological model for studying the spread of Ebola virus disease in a considered territory. This model includes the effect of various control measures, such as: vaccination, education campaigns, early detection campaigns, increase of sanitary measures in hospital, quarantine of infected individuals and restriction of movement between geographical areas. Using optimal control theory, we determine an optimal control strategy which aims to reduce the number of infected individuals, according to some operative restrictions (e.g., economical, logistic, etc.). Furthermore, we study the existence and uniqueness of the optimal control. Finally, we illustrate the interest of the obtained results by considering numerical experiments based on real data.
Collapse
Affiliation(s)
- Rama Seck
- Laboratory of Numerical Analysis and Computer Science, Applied Mathematics Section, Gaston Berger University, Saint-Louis, 209-IRD & UMMISCO-UGB, Senegal
| | - Diène Ngom
- Mathematics and Applications Laboratory, Mathematics Department, Assane Seck University, Bp: 523, Ziguinchor, 209-IRD & UMMISCO-UGB, Senegal
| | - Benjamin Ivorra
- Interdisciplinary Mathematics Institute, Department of Applied Mathematics and Mathematical Analysis, Complutense University of Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain
| | - Ángel M Ramos
- Interdisciplinary Mathematics Institute, Department of Applied Mathematics and Mathematical Analysis, Complutense University of Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain
| |
Collapse
|
10
|
DAUTEL KIMBERLYA, AGYINGI EPHRAIMO. MODELING THE IMPACT OF EDUCATIONAL CAMPAIGN ON THE TRANSMISSION DYNAMICS OF EBOLA. J BIOL SYST 2021. [DOI: 10.1142/s0218339021500248] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Disease awareness that informs the public about the severity and transmission pathways of infectious diseases such as Ebola is key to curtailing an outbreak. Public health education when available can limit the intensity and duration of an Ebola outbreak in any community if there is compliance. It is important that all population groups be informed about the methods in which Ebola is transmitted to control the disease when there is an outbreak. In this paper, we study the impact of public health education that leads to behavioral changes on the dynamics of Ebola spread. The model is formulated as a system of ordinary differential equations and incorporates direct transmission from infectious, hospitalized, and deceased individuals with Ebola. We establish the existence of a disease free equilibrium and an endemic equilibrium, and investigate them for local and global stability. Model predictions show that a more informed community results in fewer cases, and thus limits the impact of an Ebola outbreak. Further, the model also predicts subsequent outbreak waves within a community in the absence of complete eradication. Lastly, the model successfully captures the dynamics of the 2014–2016 West Africa Ebola outbreak and the 2018–2020 Democratic Republic of Congo Ebola outbreak.
Collapse
Affiliation(s)
- KIMBERLY A. DAUTEL
- School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA
| | - EPHRAIM O. AGYINGI
- School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA
| |
Collapse
|
11
|
Dhaiban AK, Jabbar BK. An optimal control model of COVID-19 pandemic: a comparative study of five countries. OPSEARCH 2021. [PMCID: PMC7814528 DOI: 10.1007/s12597-020-00491-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
This paper formulates an optimal control model of COVID-19 pandemic spreading. We discuss the health sector performance of Argentina, Hungary, Egypt, Malaysia, and Iraq. A mathematical model describes an actual case number of COVID-19. We investigate three strategies depend on recovery rate, death rate, and together (optimal). These strategies represent the percent of the health sector development. The explicit solution of the model using the Pontryagin maximum principle is derived. The results showed the ranking of countries based on the new percent of the recovery and death cases. A new percent as a result to the control variable value (health sector development). Also, the development percent of the health sector of each country, was determined. For example, 0.005 led to a significant reduce the death rates in Malaysia. Meanwhile, a half of death rates could reduce by this percent in Egypt.
Collapse
|
12
|
Vaishnav V, Vajpai J. Assessment of impact of relaxation in lockdown and forecast of preparation for combating COVID-19 pandemic in India using Group Method of Data Handling. CHAOS, SOLITONS, AND FRACTALS 2020; 140:110191. [PMID: 32834660 PMCID: PMC7413061 DOI: 10.1016/j.chaos.2020.110191] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 08/04/2020] [Indexed: 05/22/2023]
Abstract
Ever since the outbreak of novel coronavirus in December 2019, lockdown has been identified as the only effective measure across the world to stop the community spread of this pandemic. India implemented a complete shutdown across the nation from March 25, 2020 as lockdown I and went on to extend it by giving timely partial relaxations in the form of lockdown II, III & IV. This paper statistically analyses the impact of relaxation during Lockdown III and IV on coronavirus disease (COVID) spread in India using the Group Method of Data Handling (GMDH) to forecast the number of active cases using time series analysis and hence the required medical infrastructure for the period of next six months. The Group Method of Data Handling is a novel self organized data mining technique with data driven adaptive learning capability which grasps the auto correlative relations between the samples and gives a high forecasting accuracy irrespective of the length and stochasticity of a time series. The GMDH model has been first validated and standardized by forecasting the number of active and confirmed cases during lockdown III-IV with an accuracy of 2.58% and 2.00% respectively. Thereafter, the number of active cases has been forecasted for the rest of 2020 to predict the impact of lockdown relaxation on spread of COVID-19 and indicate preparatory measures necessary to counter it.
Collapse
Affiliation(s)
- Vaibhav Vaishnav
- Department of Electrical Engineering, Indian Institute of Technology, Jodhpur - 342037, India
| | - Jayashri Vajpai
- Department of Electrical Engineering, M.B.M. Engineering College, Jodhpur - 342011, India
| |
Collapse
|
13
|
Battineni G, Chintalapudi N, Amenta F. SARS-CoV-2 epidemic calculation in Italy by SEIR compartmental models. APPLIED COMPUTING AND INFORMATICS 2020. [DOI: 10.1108/aci-09-2020-0060] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Purpose
After the identification of a novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) at Wuhan, China, a pandemic was widely spread worldwide. In Italy, about 240,000 people were infected because of this virus including 34,721 deaths until the end of June 2020. To control this new pandemic, epidemiologists recommend the enforcement of serious mitigation measures like country lockdown, contact tracing or testing, social distancing and self-isolation.
Design/methodology/approach
This paper presents the most popular epidemic model of susceptible (S), exposed (E), infected (I) and recovered (R) collectively called SEIR to understand the virus spreading among the Italian population.
Findings
Developed SEIR model explains the infection growth across Italy and presents epidemic rates after and before country lockdown. The results demonstrated that follow-up of strict measures such that country lockdown along with high testing is making Italy practically a pandemic-free country.
Originality/value
These models largely help to estimate and understand how an infectious agent spreads in a particular country and how individual factors can affect the dynamics. Further studies like classical SEIR modeling can improve the quality of data and implementation of this modeling could represent a novelty of epidemic models.
Collapse
|
14
|
Carli R, Cavone G, Epicoco N, Scarabaggio P, Dotoli M. Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario. ANNUAL REVIEWS IN CONTROL 2020; 50:373-393. [PMID: 33024411 PMCID: PMC7528763 DOI: 10.1016/j.arcontrol.2020.09.005] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Revised: 09/22/2020] [Accepted: 09/24/2020] [Indexed: 05/06/2023]
Abstract
The COVID-19 outbreak is deeply influencing the global social and economic framework, due to restrictive measures adopted worldwide by governments to counteract the pandemic contagion. In multi-region areas such as Italy, where the contagion peak has been reached, it is crucial to find targeted and coordinated optimal exit and restarting strategies on a regional basis to effectively cope with possible onset of further epidemic waves, while efficiently returning the economic activities to their standard level of intensity. Differently from the related literature, where modeling and controlling the pandemic contagion is typically addressed on a national basis, this paper proposes an optimal control approach that supports governments in defining the most effective strategies to be adopted during post-lockdown mitigation phases in a multi-region scenario. Based on the joint use of a non-linear Model Predictive Control scheme and a modified Susceptible-Infected-Recovered (SIR)-based epidemiological model, the approach is aimed at minimizing the cost of the so-called non-pharmaceutical interventions (that is, mitigation strategies), while ensuring that the capacity of the network of regional healthcare systems is not violated. In addition, the proposed approach supports policy makers in taking targeted intervention decisions on different regions by an integrated and structured model, thus both respecting the specific regional health systems characteristics and improving the system-wide performance by avoiding uncoordinated actions of the regions. The methodology is tested on the COVID-19 outbreak data related to the network of Italian regions, showing its effectiveness in properly supporting the definition of effective regional strategies for managing the COVID-19 diffusion.
Collapse
Affiliation(s)
- Raffaele Carli
- Dept. of Electrical and Information Engineering, Polytechnic of Bari via Orabona 4, 70125 Bari, Italy
| | - Graziana Cavone
- Dept. of Electrical and Information Engineering, Polytechnic of Bari via Orabona 4, 70125 Bari, Italy
| | - Nicola Epicoco
- Center of Excellence DEWS, Dept. of Information Engineering, Computer Science and Mathematics, University of L'Aquila via Vetoio (Coppito 1), 67100, L'Aquila, Italy
| | - Paolo Scarabaggio
- Dept. of Electrical and Information Engineering, Polytechnic of Bari via Orabona 4, 70125 Bari, Italy
| | - Mariagrazia Dotoli
- Dept. of Electrical and Information Engineering, Polytechnic of Bari via Orabona 4, 70125 Bari, Italy
| |
Collapse
|
15
|
Abstract
In this work we present three new models of the fractal-fractional Ebola virus. We investigate the numerical solutions of the fractal-fractional Ebola virus in the sense of three different kernels based on the power law, the exponential decay and the generalized Mittag-Leffler function by using the concepts of the fractal differentiation and fractional differentiation. These operators have two parameters: The first parameter ρ is considered as the fractal dimension and the second parameter k is the fractional order. We evaluate the numerical solutions of the fractal-fractional Ebola virus for these operators with the theory of fractional calculus and the help of the Lagrange polynomial functions. In the case of ρ=k=1, all of the numerical solutions based on the power kernel, the exponential kernel and the generalized Mittag-Leffler kernel are found to be close to each other and, therefore, one of the kernels is compared with such numerical methods as the finite difference methods. This has led to an excellent agreement. For the effect of fractal-fractional on the behavior, we study the numerical solutions for different values of ρ and k. All calculations in this work are accomplished by using the Mathematica package.
Collapse
|
16
|
Singh H. Analysis for fractional dynamics of Ebola virus model. CHAOS, SOLITONS, AND FRACTALS 2020; 138:109992. [PMID: 32565622 PMCID: PMC7297191 DOI: 10.1016/j.chaos.2020.109992] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Revised: 05/08/2020] [Accepted: 06/05/2020] [Indexed: 05/04/2023]
Abstract
Ebola virus is very challenging problem of the world. The main purpose of this work is to study fractional Ebola virus model. An efficient computational method based on iterative scheme is proposed to solve fractional Ebola model numerically. Stability of proposed method is also discussed. Efficiency of proposed method is shown by listing CPU time. Proposed computational method will work for long time domain. Numerical results are presented graphically. The main reason for using this technique is low computational cost and high accuracy. It is also shown how the approximate solution varies for fractional and integer order Ebola virus model.
Collapse
Affiliation(s)
- Harendra Singh
- Department of Mathematics, Post-Graduate College, Ghazipur 233001, Uttar Pradesh, India
| |
Collapse
|
17
|
Epidemiological Modeling of COVID-19 in Saudi Arabia: Spread Projection, Awareness, and Impact of Treatment. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10175895] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
The first case of COVID-19 originated in Wuhan, China, after which it spread across more than 200 countries. By 21 July 2020, the rapid global spread of this disease had led to more than 15 million cases of infection, with a mortality rate of more than 4.0% of the total number of confirmed cases. This study aimed to predict the prevalence of COVID-19 and to investigate the effect of awareness and the impact of treatment in Saudi Arabia. In this paper, COVID-19 data were sourced from the Saudi Ministry of Health, covering the period from 31 March 2020 to 21 July 2020. The spread of COVID-19 was predicted using four different epidemiological models, namely the susceptible–infectious–recovered (SIR), generalized logistic, Richards, and Gompertz models. The assessment of models’ fit was performed and compared using four statistical indices (root-mean-square error (RMSE), R squared (R2), adjusted R2 ( Radj2), and Akaike’s information criterion (AIC)) in order to select the most appropriate model. Modified versions of the SIR model were utilized to assess the influence of awareness and treatment on the prevalence of COVID-19. Based on the statistical indices, the SIR model showed a good fit to reported data compared with the other models (RMSE = 2790.69, R2 = 99.88%, Radj2 = 99.98%, and AIC = 1796.05). The SIR model predicted that the cumulative number of infected cases would reach 359,794 and that the pandemic would end by early September 2020. Additionally, the modified version of the SIR model with social distancing revealed that there would be a reduction in the final cumulative epidemic size by 9.1% and 168.2% if social distancing were applied over the short and long term, respectively. Furthermore, different treatment scenarios were simulated, starting on 8 July 2020, using another modified version of the SIR model. Epidemiological modeling can help to predict the cumulative number of cases of infection and to understand the impact of social distancing and pharmaceutical intervention on the prevalence of COVID-19. The findings from this study can provide valuable information for governmental policymakers trying to control the spread of this pandemic.
Collapse
|
18
|
Numerical Optimal Control of HIV Transmission in Octave/MATLAB. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2019. [DOI: 10.3390/mca25010001] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70–75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge–Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge–Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article.
Collapse
|
19
|
Affiliation(s)
- Elizaveta Ermakova
- Probability Theory, Faculty of Mechanics and Mathematics, Main Building, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russian Federation
| | - Polina Makhmutova
- Probability Theory, Faculty of Mechanics and Mathematics, Main Building, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russian Federation
| | - Elena Yarovaya
- Probability Theory, Faculty of Mechanics and Mathematics, Main Building, Lomonosov Moscow State University, Leninskie Gory, Moscow, Russian Federation
| |
Collapse
|
20
|
Bao W, Michailidis G. Exponentially time decaying susceptible-informed (SIT) model for information diffusion process on networks. CHAOS (WOODBURY, N.Y.) 2018; 28:063129. [PMID: 29960402 DOI: 10.1063/1.5023925] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Modeling information diffusion on networks is a timely topic due to its significance in massive online social media platforms. Models motivated by disease epidemics, such as the Susceptible-Infected-Removed and Susceptible-Infected-Susceptible (SIS), ones have been used for this task, together with threshold models. A key limitation of these models is that the intrinsic time value of information is not accounted for, an important feature for social media applications, since "old" piece of news does not attract adequate attention. We obtain results pertaining to the diffusion size across the diffusion's evolution over time, as well as for early time points that enable us to calculate the phase transition epoch and the epidemic threshold, using mean field approximations. Further, we explicitly calculate the total probability of getting informed for each node depending on its actual path to the single seed node and then propose a novel approach by constructing a Maximum Weight Tree (MWT) to approximate the final fraction of diffusion, with the weight of each node approximating the total probability of getting informed. The MWT approximation is a novel approach that is exact for tree-like network and is specifically designed for sparse networks. It is also fast to compute and provides another general tool for the analyst to obtain accurate approximations of the "epidemic's" size. Extensive comparisons with results based on Monte Carlo simulation of the information diffusion process show that the derived mean field approximations, as well as that employing the MWT one, provide very accurate estimates of the quantities of interest.
Collapse
Affiliation(s)
- Wei Bao
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - George Michailidis
- Department of Statistics and the Institute of Informatics, University of Florida, Gainesville, Florida 32611, USA
| |
Collapse
|
21
|
Challenges of Designing and Implementing High Consequence Infectious Disease Response. Disaster Med Public Health Prep 2018; 12:563-566. [PMID: 29552993 DOI: 10.1017/dmp.2017.128] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Ebola is a high consequence infectious disease-a disease with the potential to cause outbreaks, epidemics, or pandemics with deadly possibilities, highly infectious, pathogenic, and virulent. Ebola's first reported cases in the United States in September 2014 led to the development of preparedness capabilities for the mitigation of possible rapid outbreaks, with the Centers for Disease Control and Prevention (CDC) providing guidelines to assist public health officials in infectious disease response planning. These guidelines include broad goals for state and local agencies and detailed information concerning the types of resources needed at health care facilities. However, the spatial configuration of populations and existing health care facilities is neglected. An incomplete understanding of the demand landscape may result in an inefficient and inequitable allocation of resources to populations. Hence, this paper examines challenges in implementing CDC's guidance for Ebola preparedness and mitigation in the context of geospatial allocation of health resources and discusses possible strategies for addressing such challenges. (Disaster Med Public Health Preparedness. 2018;12:563-566).
Collapse
|
22
|
Affiliation(s)
- Mario Lefebvre
- Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Montréal, Canada
| |
Collapse
|
23
|
Area I, NdaÏrou F, J. Nieto J, J. Silva C, F. M. Torres D. Ebola model and optimal control with vaccination constraints. ACTA ACUST UNITED AC 2018. [DOI: 10.3934/jimo.2017054] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
|
24
|
Berge T, Lubuma JMS, Moremedi GM, Morris N, Kondera-Shava R. A simple mathematical model for Ebola in Africa. JOURNAL OF BIOLOGICAL DYNAMICS 2017; 11:42-74. [PMID: 29067875 DOI: 10.1080/17513758.2016.1229817] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We deal with the following question: Can the consumption of contaminated bush meat, the funeral practices and the environmental contamination explain the recurrence and persistence of Ebola virus disease outbreaks in Africa? We develop an SIR-type model which, incorporates both the direct and indirect transmissions in such a manner that there is a provision of Ebola viruses. We prove that the full model has one (endemic) equilibrium which is locally asymptotically stable whereas, it is globally asymptotically stable in the absence of the Ebola virus shedding in the environment. For the sub-model without the provision of Ebola viruses, the disease dies out or stabilizes globally at an endemic equilibrium. At the endemic level, the number of infectious is larger for the full model than for the sub-model without provision of Ebola viruses. We design a nonstandard finite difference scheme, which preserves the dynamics of the model. Numerical simulations are provided.
Collapse
Affiliation(s)
- T Berge
- a Department of Mathematics and Applied Mathematics , University of Pretoria , Pretoria , South Africa
- b Department of Mathematics and Computer Sciences , University of Dschang , Dschang , Cameroon
| | - J M-S Lubuma
- a Department of Mathematics and Applied Mathematics , University of Pretoria , Pretoria , South Africa
| | - G M Moremedi
- c Department of Mathematical Sciences , University of South Africa , Pretoria , South Africa
| | - N Morris
- d Department of Forensic Medicine , University of Pretoria , Pretoria , South Africa
| | - R Kondera-Shava
- e Department of Mathematical Sciences , University of Botswana , Gaborone , Botswana
| |
Collapse
|
25
|
Levy B, Edholm C, Gaoue O, Kaondera-Shava R, Kgosimore M, Lenhart S, Lephodisa B, Lungu E, Marijani T, Nyabadza F. Modeling the role of public health education in Ebola virus disease outbreaks in Sudan. Infect Dis Model 2017; 2:323-340. [PMID: 29928745 PMCID: PMC6001965 DOI: 10.1016/j.idm.2017.06.004] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Revised: 06/01/2017] [Accepted: 06/26/2017] [Indexed: 11/01/2022] Open
Abstract
Public involvement in Ebola Virus Disease (EVD) prevention efforts is key to reducing disease outbreaks. Targeted education through practical health information to particular groups and sub-populations is crucial to controlling the disease. In this paper, we study the dynamics of Ebola virus disease in the presence of public health education with the aim of assessing the role of behavior change induced by health education to the dynamics of an outbreak. The power of behavior change is evident in two outbreaks of EVD that took place in Sudan only 3 years apart. The first occurrence was the first documented outbreak of EVD and produced a significant number of infections. The second outbreak produced far fewer cases, presumably because the population in the region learned from the first outbreak. We derive a system of ordinary differential equations to model these two contrasting behaviors. Since the population in Sudan learned from the first outbreak of EVD and changed their behavior prior to the second outbreak, we use data from these two instances of EVD to estimate parameters relevant to two contrasting behaviors. We then simulate a future outbreak of EVD in Sudan using our model that contains two susceptible populations, one being more informed about EVD. Our finding show how a more educated population results in fewer cases of EVD and highlights the importance of ongoing public health education.
Collapse
Affiliation(s)
- Benjamin Levy
- Department of Mathematics, Fitchburg State University, USA
| | | | - Orou Gaoue
- Department of Botany, University of Hawaii, USA
| | | | - Moatlhodi Kgosimore
- Department of Basic Sciences, Botswana University of Agriculture and Natural Resources, Botswana
| | | | | | - Edward Lungu
- Department of Mathematics, Botswana International University of Science and Technology, Botswana
| | | | - Farai Nyabadza
- Department of Mathematics, University of Stellenbosch, South Africa
| |
Collapse
|
26
|
Khaleque A, Sen P. An empirical analysis of the Ebola outbreak in West Africa. Sci Rep 2017; 7:42594. [PMID: 28205617 PMCID: PMC5311974 DOI: 10.1038/srep42594] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Accepted: 01/11/2017] [Indexed: 11/09/2022] Open
Abstract
The data for the Ebola outbreak that occurred in 2014–2016 in three countries of West Africa are analysed within a common framework. The analysis is made using the results of an agent based Susceptible-Infected-Removed (SIR) model on a Euclidean network, where nodes at a distance l are connected with probability P(l) ∝ l−δ, δ determining the range of the interaction, in addition to nearest neighbors. The cumulative (total) density of infected population here has the form , where the parameters depend on δ and the infection probability q. This form is seen to fit well with the data. Using the best fitting parameters, the time at which the peak is reached is estimated and is shown to be consistent with the data. We also show that in the Euclidean model, one can choose δ and q values which reproduce the data for the three countries qualitatively. These choices are correlated with population density, control schemes and other factors. Comparing the real data and the results from the model one can also estimate the size of the actual population susceptible to the disease. Rescaling the real data a reasonably good quantitative agreement with the simulation results is obtained.
Collapse
Affiliation(s)
- Abdul Khaleque
- Department of Physics, University of Calcutta, 92 APC Road, Kolkata 700009, India
| | - Parongama Sen
- Department of Physics, University of Calcutta, 92 APC Road, Kolkata 700009, India
| |
Collapse
|
27
|
Rachah A, Torres DFM. Dynamics and Optimal Control of Ebola Transmission. MATHEMATICS IN COMPUTER SCIENCE 2016. [DOI: 10.1007/s11786-016-0268-y] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
|
28
|
Bonyah E, Badu K, Asiedu-Addo SK. Optimal control application to an Ebola model. Asian Pac J Trop Biomed 2016; 6:283-289. [PMID: 32289024 PMCID: PMC7103935 DOI: 10.1016/j.apjtb.2016.01.012] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Revised: 12/23/2015] [Accepted: 01/04/2016] [Indexed: 01/19/2023] Open
Abstract
Ebola virus is a severe, frequently fatal illness, with a case fatality rate up to 90%. The outbreak of the disease has been acknowledged by World Health Organization as Public Health Emergency of International Concern. The threat of Ebola in West Africa is still a major setback to the socioeconomic development. Optimal control theory is applied to a system of ordinary differential equations which is modeling Ebola infection through three different routes including contact between humans and a dead body. In an attempt to reduce infection in susceptible population, a preventive control is put in the form of education and campaign and two treatment controls are applied to infected and late-stage infected (super) human population. The Pontryagins maximum principle is employed to characterize optimality control, which is then solved numerically. It is observed that time optimal control is existed in the model. The activation of each control showed a positive reduction of infection. The overall effect of activation of all the controls simultaneously reduced the effort required for the reduction of the infection quickly. The obtained results present a good framework for planning and designing cost-effective strategies for good interventions in dealing with Ebola disease. It is established that in order to reduce Ebola threat all the three controls must be taken into consideration concurrently.
Collapse
Affiliation(s)
- Ebenezer Bonyah
- Department of Mathematics and Statistics, Kumasi Polytechnic, Kumasi, Ghana
| | - Kingsley Badu
- Noguchi Memorial Institute for Medical Research, College of Health Science, University of Ghana, Legon, Accra, Ghana
- Faculty of Health Sciences, Garden City University College, Kenyase, Kumasi, Ghana
| | | |
Collapse
|
29
|
Rachah A, Torres DFM. Predicting and controlling the Ebola infection. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2016. [DOI: 10.1002/mma.3841] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- Amira Rachah
- Institut de Mathématiques; Université Paul Sabatier; Toulouse 31062, Cedex 9 France
| | - Delfim F. M. Torres
- Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics; University of Aveiro; Aveiro 3810-193 Portugal
| |
Collapse
|
30
|
Optimal Intervention Strategies for a SEIR Control Model of Ebola Epidemics. MATHEMATICS 2015. [DOI: 10.3390/math3040961] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|