ODE AND PDE MODELS FOR COVID-19, WITH REINFECTION AND VACCINATION PROCESS FOR CAMEROON AND GERMANY

Abboubakar H, Racke R, Schlosser N (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Discrete and Continuous Dynamical Systems-Series B American Institute of Mathematical Sciences (AIMS)

Book Volume: 36

Pages Range: 304-336

DOI: 10.3934/dcdsb.2026034

Abstract

We develop and analyze a reaction-diffusion model for the transmission dynamics of the coronavirus (COVID-19) that accounts for reinfection and vaccination, and compare it to the ODE model. For the latter, we calculate the control reproduction number ℛc and demonstrate the global stability of the DFE for ℛc<1. We also show that when ℛc>1, the DFE becomes unstable and co-exists with at least one endemic equilibrium point. We use data from Germany and Cameroon to calibrate our model. We find ℛc≈1.13 for Germany and ℛc≈1.2554 for Cameroon, indicating a persistence of the disease. We use sensitivity analysis (SA) to identify model factors that contribute to the disease dynamics. According to this analysis, the most crucial factors are the transmission rate, the recovered rate of asymptomatic humans, and the recovered rate of symptomatic humans. Then, a modification to a reaction-diffusion PDE model, accounting for spatial mobility, is studied; solutions exist and are non-negative and unique. The DFE is locally stable, and globally stable when ℛc<1. For ℛc>1, the DFE is unstable and coexists with at least one endemic equilibrium point. Numerical simulations validate our theoretical predictions. We then compare the ODE and PDE models.

Involved external institutions

University of Ngaoundéré / Universitè de Ngaoundéré CM Cameroon (CM) Universität Konstanz DE Germany (DE)

How to cite

APA:

Abboubakar, H., Racke, R., & Schlosser, N. (2026). ODE AND PDE MODELS FOR COVID-19, WITH REINFECTION AND VACCINATION PROCESS FOR CAMEROON AND GERMANY. Discrete and Continuous Dynamical Systems-Series B, 36, 304-336. https://doi.org/10.3934/dcdsb.2026034

MLA:

Abboubakar, Hamadjam, Reinhard Racke, and Nicolas Schlosser. "ODE AND PDE MODELS FOR COVID-19, WITH REINFECTION AND VACCINATION PROCESS FOR CAMEROON AND GERMANY." Discrete and Continuous Dynamical Systems-Series B 36 (2026): 304-336.

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