Existence of Traveling Waves of a Diffusive Susceptible–Infected–Symptomatic–Recovered Epidemic Model with Temporal Delay

Abstract

The aim of this article is to investigate the existence of traveling waves of a diffusive model that represents the transmission of a virus in a determined population composed of the following populations: susceptible (S), infected (I), asymptomatic (A), and recovered (R). An analytical study is performed, where the existence of solutions of traveling waves in a bounded domain is demonstrated. We use the upper and lower coupled solutions method to achieve this aim. The existence and local asymptotic stability of the endemic (Ee) and disease-free (E0) equilibrium states are also determined. The constructed model includes a discrete-time delay that is related to the incubation stage of a virus. We find the crucial basic reproduction number R0, which determines the local stability of the steady states. We perform numerical simulations of the model in order to provide additional support to the theoretical results and observe the traveling waves. The model can be used to study the dynamics of SARS-CoV-2 and other viruses where the disease evolution has a similar behavior.

Dynamics of Infectious Diseases Incorporating a Testing Compartment

“…Many model studies [3][4][5][6][7][8][9][10][11][12] have been done on the COVID-19 outbreak to investigate its transmission dynamics. The modeling studies are mostly based on the classic Susceptible-Infected-Recovered (SIR) compartmental model [1] in epidemiology.…”

“…Parameter c is the disease transmission rate and r is the recovery rate. In [3], the authors added an asymptomatic (A) compartment in a diffusion model to study the dynamics of COVID-19 and determined the existence and local asymptotic stability of the endemic and disease-free equilibrium states. Other research works incorporated at least one exposed (E) compartment to study COVID-19 transmission [4][5][6][7][8][9], where [4] also took into account the hospitalized compartment to emphasize the vulnerable people in the population group, ref.…”