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Marín-Machuca O, Chacón RD, Alvarez-Lovera N, Pesantes-Grados P, Pérez-Timaná L, Marín-Sánchez O. Mathematical Modeling of COVID-19 Cases and Deaths and the Impact of Vaccinations during Three Years of the Pandemic in Peru. Vaccines (Basel) 2023; 11:1648. [PMID: 38005980 PMCID: PMC10674587 DOI: 10.3390/vaccines11111648] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2023] [Revised: 09/27/2023] [Accepted: 09/29/2023] [Indexed: 11/26/2023] Open
Abstract
The COVID-19 pandemic has caused widespread infections, deaths, and substantial economic losses. Vaccine development efforts have led to authorized candidates reducing hospitalizations and mortality, although variant emergence remains a concern. Peru faced a significant impact due to healthcare deficiencies. This study employed logistic regression to mathematically model COVID-19's dynamics in Peru over three years and assessed the correlations between cases, deaths, and people vaccinated. We estimated the critical time (tc) for cases (627 days), deaths (389 days), and people vaccinated (268 days), which led to the maximum speed values on those days. Negative correlations were identified between people vaccinated and cases (-0.40) and between people vaccinated and deaths (-0.75), suggesting reciprocal relationships between those pairs of variables. In addition, Granger causality tests determined that the vaccinated population dynamics can be used to forecast the behavior of deaths (p-value < 0.05), evidencing the impact of vaccinations against COVID-19. Also, the coefficient of determination (R2) indicated a robust representation of the real data. Using the Peruvian context as an example case, the logistic model's projections of cases, deaths, and vaccinations provide crucial insights into the pandemic, guiding public health tactics and reaffirming the essential role of vaccinations and resource distribution for an effective fight against COVID-19.
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Affiliation(s)
- Olegario Marín-Machuca
- Departamento Académico de Ciencias Alimentarias, Facultad de Oceanografía, Pesquería, Ciencias Alimentarias y Acuicultura, Universidad Nacional Federico Villarreal, Calle Roma 350, Miraflores 15074, Peru;
| | - Ruy D. Chacón
- Department of Pathology, School of Veterinary Medicine, University of São Paulo, Av. Prof. Orlando M. Paiva, 87, São Paulo 05508-270, Brazil
| | - Natalia Alvarez-Lovera
- Escuela Profesional de Genética y Biotecnología, Facultad de Ciencias Biológicas, Universidad Nacional Mayor de San Marcos, Av. Carlos Germán Amezaga 375, Lima 15081, Peru; (N.A.-L.); (L.P.-T.)
| | - Pedro Pesantes-Grados
- Unidad de Posgrado, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Av. Carlos Germán Amezaga 375, Lima 15081, Peru;
| | - Luis Pérez-Timaná
- Escuela Profesional de Genética y Biotecnología, Facultad de Ciencias Biológicas, Universidad Nacional Mayor de San Marcos, Av. Carlos Germán Amezaga 375, Lima 15081, Peru; (N.A.-L.); (L.P.-T.)
| | - Obert Marín-Sánchez
- Departamento Académico de Microbiología Médica, Facultad de Medicina, Universidad Nacional Mayor de San Marcos, Av. Carlos Germán Amezaga 375, Lima 15081, Peru
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Implementation of computationally efficient numerical approach to analyze a Covid-19 pandemic model. ALEXANDRIA ENGINEERING JOURNAL 2023; 69:341-362. [PMCID: PMC9918432 DOI: 10.1016/j.aej.2023.01.052] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Revised: 01/05/2023] [Accepted: 01/23/2023] [Indexed: 09/17/2023]
Abstract
Corona virus disease (Covid-19) which has caused frustration in the human community remains the concern of the globe as every government struggles to defeat the pandemic. To deal with the situation, we have extensively studied a deadly Covid-19 model to provide a deep insight into the disease dynamics. A mathematical analysis of the model utilizing preventive measures is performed with the aim to reduce the disease burden. Some comprehensive mathematical techniques are employed to demonstrate several essential properties of solutions. To start with, we proved the existence and uniqueness of solutions. Equilibrium points are stated both in the absence and presence of the pandemic. Biologically important quantity known as threshold parameter is computed to handle the future disease dynamics and analyzed for its sensitivity. We proved the stability of the proposed model at equilibrium points by employing necessary conditions on threshold parameter. A reliable and competitive numerical analysis is conducted to observe the effectiveness of implemented strategies and to verify obtained analytical results. The most sensitive parameters are determined through sensitivity analysis. An important feature of this study is to employ Non-Standard Finite Difference (NSFD) numerical scheme to solve the system instead of other standard methods like Runge–Kutta method of order 4 (RK4). Finally, several numerical simulations are performed to validate our former theoretical analysis. Numerical results exhibiting dynamical behavior of Covid-19 system under the influence of involved parameters suggest that both the implemented strategies, especially quarantine of exposed individuals, are effective for the substantial reduction in the diseased population and to achieve the herd immunity.
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Prem Kumar R, Santra PK, Mahapatra GS. Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive. MATHEMATICS AND COMPUTERS IN SIMULATION 2023; 203:741-766. [PMID: 35911951 PMCID: PMC9308141 DOI: 10.1016/j.matcom.2022.07.012] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 07/13/2022] [Accepted: 07/13/2022] [Indexed: 05/25/2023]
Abstract
The study explores the dynamics of a COVID-19 epidemic in multiple susceptible populations, including the various stages of vaccination administration. In the model, there are eight human compartments: completely susceptible; susceptible with dose-1 vaccination; susceptible with dose-2 vaccination; susceptible with booster dose vaccination; exposed; infected with and without symptoms, and recovered compartments. The biological feasibility of the model is analysed. The threshold value,R 0 , is derived using the next-generation matrix. The stability analysis of the equilibrium points was performed locally and globally using the threshold parameter of the model. The conditions determining disease persistence is obtained. The model is subjected to sensitivity analysis, and the most sensitive parameters are identified. Also, MATLAB is used to verify the mathematical outcomes of the system's dynamic behaviour and suggests that necessary steps should be taken to keep the spread of the omicron variant infectious disease under control. The findings of this study could aid health officials in their efforts to combat the spread of COVID-19.
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Affiliation(s)
- R Prem Kumar
- Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India
- Department of Mathematics, Avvaiyar Government College for Women, Karaikal 609602, Puducherry, India
| | - P K Santra
- Moulana Abul Kalam Azad University of Technology, Kolkata 700064, India
| | - G S Mahapatra
- Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India
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Nonlinear model of infection wavy oscillation of COVID-19 in Japan based on diffusion kinetics. Sci Rep 2022; 12:19177. [PMID: 36357499 PMCID: PMC9647254 DOI: 10.1038/s41598-022-23633-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2022] [Accepted: 11/02/2022] [Indexed: 11/11/2022] Open
Abstract
The infectious propagation of SARS-CoV-2 is continuing worldwide, and specifically, Japan is facing severe circumstances. Medical resource maintenance and action limitations remain the central measures. An analysis of long-term follow-up reports in Japan shows that the infection number follows a unique wavy oscillation, increasing and decreasing over time. However, only a few studies explain the infection wavy oscillation. This study introduces a novel nonlinear mathematical model of the new infection wavy oscillation by applying the macromolecule diffusion theory. In this model, the diffusion coefficient that depends on population density gives nonlinearity in infection propagation. As a result, our model accurately simulated infection wavy oscillations, and the infection wavy oscillation frequency and amplitude were closely linked with the recovery rate of infected individuals. In conclusion, our model provides a novel nonlinear contact infection analysis framework.
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Kong L, Duan M, Shi J, Hong J, Chang Z, Zhang Z. Compartmental structures used in modeling COVID-19: a scoping review. Infect Dis Poverty 2022; 11:72. [PMID: 35729655 PMCID: PMC9209832 DOI: 10.1186/s40249-022-01001-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2022] [Accepted: 06/10/2022] [Indexed: 12/23/2022] Open
Abstract
Background The coronavirus disease 2019 (COVID-19) epidemic, considered as the worst global public health event in nearly a century, has severely affected more than 200 countries and regions around the world. To effectively prevent and control the epidemic, researchers have widely employed dynamic models to predict and simulate the epidemic’s development, understand the spread rule, evaluate the effects of intervention measures, inform vaccination strategies, and assist in the formulation of prevention and control measures. In this review, we aimed to sort out the compartmental structures used in COVID-19 dynamic models and provide reference for the dynamic modeling for COVID-19 and other infectious diseases in the future. Main text A scoping review on the compartmental structures used in modeling COVID-19 was conducted. In this scoping review, 241 research articles published before May 14, 2021 were analyzed to better understand the model types and compartmental structures used in modeling COVID-19. Three types of dynamics models were analyzed: compartment models expanded based on susceptible-exposed-infected-recovered (SEIR) model, meta-population models, and agent-based models. The expanded compartments based on SEIR model are mainly according to the COVID-19 transmission characteristics, public health interventions, and age structure. The meta-population models and the agent-based models, as a trade-off for more complex model structures, basic susceptible-exposed-infected-recovered or simply expanded compartmental structures were generally adopted. Conclusion There has been a great deal of models to understand the spread of COVID-19, and to help prevention and control strategies. Researchers build compartments according to actual situation, research objectives and complexity of models used. As the COVID-19 epidemic remains uncertain and poses a major challenge to humans, researchers still need dynamic models as the main tool to predict dynamics, evaluate intervention effects, and provide scientific evidence for the development of prevention and control strategies. The compartmental structures reviewed in this study provide guidance for future modeling for COVID-19, and also offer recommendations for the dynamic modeling of other infectious diseases. Graphical Abstract
Supplementary Information The online version contains supplementary material available at 10.1186/s40249-022-01001-y.
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Affiliation(s)
- Lingcai Kong
- Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China
| | - Mengwei Duan
- Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China
| | - Jin Shi
- Department of Epidemiology and Health Statistics, Fudan University, Shanghai, 200032, China
| | - Jie Hong
- Department of Epidemiology and Health Statistics, Fudan University, Shanghai, 200032, China
| | - Zhaorui Chang
- Division of Infectious Disease, Key Laboratory of Surveillance and Early-Warning on Infectious Disease, Chinese Center for Disease Control and Prevention, Beijing, China
| | - Zhijie Zhang
- Department of Epidemiology and Health Statistics, Fudan University, Shanghai, 200032, China.
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Kumar RP, Basu S, Santra P, Ghosh D, Mahapatra G. Optimal control design incorporating vaccination and treatment on six compartment pandemic dynamical system. RESULTS IN CONTROL AND OPTIMIZATION 2022. [PMCID: PMC8969442 DOI: 10.1016/j.rico.2022.100115] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
In this paper, a mathematical model of the COVID-19 pandemic with lockdown that provides a more accurate representation of the infection rate has been analyzed. In this model, the total population is divided into six compartments: the susceptible class, lockdown class, exposed class, asymptomatic infected class, symptomatic infected class, and recovered class. The basic reproduction number (R0) is calculated using the next-generation matrix method and presented graphically based on different progression rates and effective contact rates of infective individuals. The COVID-19 epidemic model exhibits the disease-free equilibrium and endemic equilibrium. The local and global stability analysis has been done at the disease-free and endemic equilibrium based on R0. The stability analysis of the model shows that the disease-free equilibrium is both locally and globally stable when R0<1, and the endemic equilibrium is locally and globally stable when R0>1 under some conditions. A control strategy including vaccination and treatment has been studied on this pandemic model with an objective functional to minimize. Finally, numerical simulation of the COVID-19 outbreak in India is carried out using MATLAB, highlighting the usefulness of the COVID-19 pandemic model and its mathematical analysis.
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Cooper I, Mondal A, Antonopoulos CG, Mishra A. Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model. NONLINEAR DYNAMICS 2022; 109:19-32. [PMID: 35340759 PMCID: PMC8933770 DOI: 10.1007/s11071-022-07347-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/02/2021] [Accepted: 03/05/2022] [Indexed: 06/14/2023]
Abstract
In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible-infected-removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.
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Affiliation(s)
- Ian Cooper
- School of Physics, The University of Sydney, Sydney, Australia
| | - Argha Mondal
- Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal 723104 India
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK
| | - Chris G. Antonopoulos
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK
| | - Arindam Mishra
- Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924 Lodz, Poland
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