Modeling individual mobility’s impact on COVID-19 transmission: Insights from a two-patch SEIR-V approach

Document Type : Research Article

Authors

• M. Bouziane ¹
• M.A. Boubekeur ²
• M.E.B. Keddar ²
• O. Belhamiti ²

¹ Department of Mathematics, Higher Normal School of Mostaganem, Mostaganem 27000, Algeria.

² Department of Mathematics and Computer Science, Abdelhamid Ben Badis University, Mostaganem 27000, Algeria.

10.22067/ijnao.2024.85987.1365

Abstract

This research explores the influence of individual mobility on COVID-19 transmission, utilizing a temporal mathematical model to clarify disease spread and vaccination dynamics across diverse regions. Employing a com-putationally efficient two-patch configuration that emphasizes regional in-teractions, our study aims to guide optimal disease control strategies. The introduced SEIR-V model with a two-patch setup estimates the vaccination reproduction number, Rv, while equilibrium points and system stability are identified. Visualizations from numerical simulations and sensitivity analyses illustrate key parameters affecting the vaccination reproduction number and COVID-19 control measures. Our findings underscore system responsiveness, emphasizing the intricate relationship between Rv , migra-tion rates, and disease prevalence.

Keywords

• COVID-19
• Metapopulation
• Global stability
• Local stability
• Vaccination reproduction number

Main Subjects

• Modeling and Simulation

---

References

[1] Ahmad, R.A., Imron, M.A., Ramadona, A.L., Lathifah, N., Azzahra, F., Widyastuti, K. and Fuad, A. Modeling social interaction and metapop-ulation mobility of the COVID-19 pandemic in main cities of highly populated Java Island, Indonesia: An agent-based modeling approach, Front. Ecol. Evol. 10 (2023), 958651.
[2] Arino, J., Sun, C. and Yang, W. Revisiting a two-patch SIS model with infection during transport, Math. Med. Biol. 33(1) (2015), 29–55.
[3] Arino, J. and Van Den Driessche, P. Disease spread in metapopulations, Fields Inst. Commun. 48 (2006), 1–12.
[4] Baister, M., McTaggart, E., McMenemy, P., Megiddo, I. and Kleczkowski, A. COVID-19 in Scottish care homes: A metapop-ulation model of spread among residents and staff, medRxiv 2021.08.24.21262524.
[5] Bortolatto, R. A note on the Lienard-Chipart criterion and roots of some families of polynomials, arXiv preprint arXiv:1407.4852 (2014).
[6] Boubekeur, M.A. and Belhamiti, O. Modeling the Impact of Obesity on COVID-19: Evidence from Sensitivity Analysis, (2023), Submitted.
[7] Bouziane, M., Mezouaghi, A. and Belhamiti, O. analysis of the vac-cination reproduction number and endemic equilibrium to control the Covid-19 spread, Adv. Math. Sci. App. 32(2) (2023), 399–430.
[8] Castillo-Chavez, C. and Thieme, H. Autonomous epidemic models, O. Arino, D. Axelrod, M. Kimmel, M. Langlais (Eds.), Mathematical Pop-ulation Dynamics: Analysis of Heterogeneity, BU-1248-M (1994) 1–23.

[9] Chen, T.M., Rui, J., Wang, Q.P., Zhao, Z.Y., Cui, J.A. and Yin, L.A. Model for simulating the phase-based transmissibility of a novel coron-avirus, Infect. Dis. Poverty 9(1) (2020), 1–8.
[10] Chitnis, N., Hyman, J.M. and Cushing, J.M. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol. 70 (2008), 1272–1296.
[11] Daud, A.A.M. A note on Lienard-Chipart criteria and its application to epidemic models, Mathematics and Statistics 9 (2021), 41–45.
[12] Faiçal, N., Ivan, A., Juan, N. and Delfim, T. Modeling of COVID-19 transmission dynamics with a case study of Wuhan, Chaos Solit. Fractals. 135 (2020), 109846.
[13] Hancean, M.G., Slavinec, M. and Perc, M. impact of human mobility networks on the global spread of COVID-19, J. Complex Netw. 8(6) (2020), 1–14.
[14] Humphries, R., Spillane, M., Mulchrone, K., Wieczorek, S., Riordain, M. and Havel, P. A metapopulation network model for the spreading of SARS CoV-2: Case study for Ireland, Infect. Dis. Model. 6 (2021), 420–437.
[15] Iyaniwura, S.A., Ringa, N., Adu, P.A., Mak, S., Janjua, N.Z., Irvine, M.A. and Otterstatter, M. Understanding the impact of mobility on COVID-19 spread: A hybrid gravity-metapopulation model of COVID-19, PLoS Comput. Biol. 19(5) (2023), e1011123.
[16] Keddar, M.E.B. and Belhamiti O. A study of global dynamics and sensi-tivity analysis of a discrete-time model of the COVID-19 epidemic, Ira-nian Journal of Numerical Analysis and Optimization (2023), Accepted. 10.22067/IJNAO.2023.82954.1281
[17] Kim, J.H., SU, W. and Song, Y.J. On stability of a polynomial, J. Appl. Math. Inform. 36 (2018), 231–236.
[18] Knobler, S., Mahmoud, A., Lemon, S. and Pray, L. The impact of glob-alization on infectious disease emergence and control: Exploring the con-sequences and opportunities, Workshop Summary - Forum on Microbial Threats, The National Academies Press, 2006.
[19] Lan Meng, L. and Zhu, W. SEIR epidemic model for COVID-19 in a multipatch environment, discrete dynamics in nature society, Discrete Dyn. Nature Soc. 2021 (2021), Article ID 5401253, 1–12.
[20] Martens, P. and Hall, L. Malaria on the move: human population move-ment and malaria transmission, Emerg. Infect. Dis. 6 (2) (2000), 103–109.
[21] McCarthy, C.V., O’Mara, O. and Van Leeuwen, E. The impact of COVID-19 vaccination in prisons in England and Wales: a metapopu-lation model, BMC Public Health, 22 (1003) (2022), 1–17.
[22] Perlman, S., Another decade, another Coronavirus, N. Engl. J. Med. 382(8) (2020), 760–762.
[23] Rabitz, H., Kramer, M. and Dacol, D. Sensitivity analysis in chemical kinetics, Annu. Rev. Phys. Chem. 34 (1983), 419–461.
[24] Smith, H.L. and Waltman, P. The theory of the Chemostat, Cambridge University, 1995.
[25] Van Den Driessche, P. Reproduction numbers of infectious disease mod-els, Infect. Dis. Model. 2 (2017), 288–303.
[26] Van Den Driessche, P. and Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29–48.
[27] Van Den Driessche, P. and Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci 180 (2002), 29–48.
[28] World Health Organization (WHO). Coronavirus (COVID-19) Dash-board; (accessed April 17, 2022).
[29] World Health Organization (WHO). Novel Coronavirus 2019-nCoV, sit-uation report-1. (accessed May 10, 2021).

[30] Zhao, X. Systems in population biology, Springer, 2003.
[31] Zi, Z. Sensitivity analysis approaches applied to systems biology models, IET Syst. Biol. 5 (2011), 336–346.