Longtime behaviors of an epidemic model with nonlocal diffusions and a free boundary: rate of accelerated spreading

TL;DR

This paper investigates the accelerated spreading rates in an epidemic model with nonlocal diffusion and free boundaries, revealing how kernel tail heaviness influences the speed of epidemic spread.

Contribution

It provides new insights into the spreading dynamics by establishing the relationship between kernel tail behavior and acceleration rate, along with refined spreading profiles.

Findings

Heavier kernel tails lead to faster spreading rates.

Constructed upper and lower solutions to determine spreading speed.

Obtained more precise profiles for the epidemic components.

Abstract

This is the third part of our series of work devoted to the dynamics of an epidemic model with nonlocal diffusions and free boundary. This part is concerned with the rate of accelerated spreading for three types of kernel functions when spreading happens. By constructing the suitable upper and lower solutions, we get the rate of the accelerated spreading of free boundary, which is closely related to the behavior of kernel functions near infinity. Our results indicate that the heavier the tail of the kernel functions are, the faster the rate of accelerated spreading is. Moreover, more accurate spreading profiles for solution component $(u,v)$ are also obtained.