Modeling and Simulating an Epidemic in Two Dimensions with an Application Regarding COVID-19

Abstract

We derive a reaction–diffusion model with time-delayed nonlocal effects to study an epidemic’s spatial spread numerically. The model describes infected individuals in the latent period using a structured model with diffusion. The epidemic model assumes that infectious individuals are subject to containment measures. To simulate the model in two-dimensional space, we use the continuous Runge–Kutta method of the fourth order and the discrete Runge–Kutta method of the third order with six stages. The numerical results admit the existence of traveling wave solutions for the proposed model. We use the COVID-19 epidemic to conduct numerical experiments and investigate the minimal speed of spread of the traveling wave front. The minimal spreading speeds of COVID-19 are found and discussed. Also, we assess the power of containment measures to contain the epidemic. The results depict a clear drop in the spreading speed of the traveling wave front after applying containment measures to at-risk populations.

Keywords

• epidemic of COVID-19
• incubation period
• continuous Runge–Kutta method
• traveling wave solution
• spreading speed
• delay model