In this paper, we develop a mathematical model for the spread of COVID-19 outbreak, taking into account vaccination in susceptible and recovered populations. The model divides the population into eight classes, including susceptible, vaccinated in S class, exposed, infected asymptomatic, infected symptomatic, hospitalized, recovery, and vaccinated in recovered class. By applying a vaccine-distribution scenario, we investigate the impact of vaccines on the COVID-19 outbreak. After analyzing the equilibrium point and computing the basic reproduction number, we perform numerical simulation and sensitivity analysis to identify the most influential parameters and evaluate the impact of vaccine distribution on policies to control the spread of COVID-19. Our findings suggest that vaccine distribution can effectively suppress the spread of COVID-19, and increasing the $ v $ parameter (vaccine distribution) and $ \alpha_1 $ parameter (acceleration of detection of undetected infected individuals who have recovered) can help control the outbreak. Moreover, decreasing the contact between vulnerable and infected individuals can lower the $ \beta_{1} $ parameter, leading to $ R_0 < 1 $, which indicates a disease-free population. This study contributes to understanding the impact of vaccination on the spread of COVID-19 and provides insights for policymakers in developing control strategies.
Citation: Moh. Mashum Mujur Ihsanjaya, Nanang Susyanto. A mathematical model for policy of vaccinating recovered people in controlling the spread of COVID-19 outbreak[J]. AIMS Mathematics, 2023, 8(6): 14508-14521. doi: 10.3934/math.2023741
In this paper, we develop a mathematical model for the spread of COVID-19 outbreak, taking into account vaccination in susceptible and recovered populations. The model divides the population into eight classes, including susceptible, vaccinated in S class, exposed, infected asymptomatic, infected symptomatic, hospitalized, recovery, and vaccinated in recovered class. By applying a vaccine-distribution scenario, we investigate the impact of vaccines on the COVID-19 outbreak. After analyzing the equilibrium point and computing the basic reproduction number, we perform numerical simulation and sensitivity analysis to identify the most influential parameters and evaluate the impact of vaccine distribution on policies to control the spread of COVID-19. Our findings suggest that vaccine distribution can effectively suppress the spread of COVID-19, and increasing the $ v $ parameter (vaccine distribution) and $ \alpha_1 $ parameter (acceleration of detection of undetected infected individuals who have recovered) can help control the outbreak. Moreover, decreasing the contact between vulnerable and infected individuals can lower the $ \beta_{1} $ parameter, leading to $ R_0 < 1 $, which indicates a disease-free population. This study contributes to understanding the impact of vaccination on the spread of COVID-19 and provides insights for policymakers in developing control strategies.
| [1] | Reported cases and deaths by country or territory, 2022. Available from: https://www.worldometers.info/coronavirus/. |
| [2] | Map of spread of COVID-19, 2022. Available from: https://covid19.go.id/peta-sebaran-covid19. |
| [3] |
N. Nuraini, K. Khairudin, M. Apri, Modeling simulation of COVID-19 in indonesia based on early endemic data, Cummun. Biomath. Sci., 3 (2020), 1–8. https://doi.org/10.5614/cbms.2020.3.1.1 doi: 10.5614/cbms.2020.3.1.1
|
| [4] |
A. Suwardi, M. Isbar, M. Rifandi, Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia, Chaos Solitons Fract., 139 (2020), 110072. https://doi.org/10.1016/j.chaos.2020.110072 doi: 10.1016/j.chaos.2020.110072
|
| [5] | H. Susanto, Kalau kita tidak serius puncak COVID-19 di Indonesia bisa sekitar 2 bulan lagi, di bulan Ramadan, Tech. Rep., 2020, 1–3. |
| [6] |
N. Nuraini, K. K. Sukandar, P. Hadisoemarto, H. Susanto, A. I. Hasan, N. Sumarti, Mathematical models for assessing vaccination scenarios in several provinces in indonesia, Infect. Dis. Modell., 6 (2021), 1236–1258. https://doi.org/10.1016/j.idm.2021.09.002 doi: 10.1016/j.idm.2021.09.002
|
| [7] |
Z. Mukandavire, F. Nyabadza, N. J. Malunguza, D. F. Cuadros, T. Shiri, G. Musuka, Quantifying early COVID-19 outbreak transmission in South Africa and exploring vaccine efficacy scenarios, PLoS One, 15 (2020), e0236003. https://doi.org/10.1371/journal.pone.0236003 doi: 10.1371/journal.pone.0236003
|
| [8] |
A. Din, Y. Li, T. Khan, G. Zaman, Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China, Chaos Solitons Fract., 141 (2020), 110286. https://doi.org/10.1016/j.chaos.2020.110286 doi: 10.1016/j.chaos.2020.110286
|
| [9] |
A. Din, The stochastic bifurcation analysis and stochastic delayed optimal control for epidemic model with general incidence function, Chaos, 31 (2021), 123101. https://doi.org/10.1063/5.0063050 doi: 10.1063/5.0063050
|
| [10] |
M. L. Diagne, H. Rwezaura, S. Y. Tchoumi, J. M. Tchuenche, A mathematical model of COVID-19 with vaccination and treatment, Comput. Math. Methods Med., 2021 (2021), 1250129. https://doi.org/10.1155/2021/1250129 doi: 10.1155/2021/1250129
|
| [11] |
O. Diekmann, J. A. Heesterbeek, J. A. Metz, On the definition and the computation of the basic reproduction ratio R$_{0}$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365–382. https://doi.org/10.1007/BF00178324 doi: 10.1007/BF00178324
|
| [12] |
P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartemental model of disease transmission, Math. Biosci., 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
|
| [13] |
D. Aldila, S. Khoshnaw, E. Safitri, A mathematical study on the spread of COVID-19 considering social distancing and rapid assessment: the case of Jakarta, Indonesia, Chaos Solitons Fract., 139 (2020), 110042. https://doi.org/10.1016/j.chaos.2020.110042 doi: 10.1016/j.chaos.2020.110042
|
Figures(8) / Tables(3)
Moh. Mashum Mujur Ihsanjaya, Nanang Susyanto. A mathematical model for policy of vaccinating recovered people in controlling the spread of COVID-19 outbreak[J]. AIMS Mathematics, 2023, 8(6): 14508-14521. doi: 10.3934/math.2023741
DownLoad: