Dynamics analysis of a spatiotemporal SI model

In this article, we investigate a susceptible-infected (SI) model with the saturated treatment, the non-monotonic incidence rate, the logistic growth, and the homogeneous Neumann boundary conditions. The global existence and the uniform boundedness of the parabolic system are performed. After that, we investigate the global stability of the disease free equilibrium (DFE) and the endemic equilibrium (EE), respectively. In the end, we give a priori estimates, some propositions of the nonconstant steady states to the elliptic system. Meanwhile, we find that the diffusion rates of the susceptible and the infected population can affect the nonexistence of the nonconstant steady states. An interesting finding is DFE and basic reproduction number do not exist when the intrinsic growth rate of the susceptible class less than the rate of susceptible individuals being vaccinated.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

This article investigates an SI model with saturated treatment, non-monotonic incidence rate, logistic growth, and homogeneous Neumann boundary conditions. The global existence and uniform boundedness of the parabolic system are analyzed. The global stability of the disease-free and endemic equilibria are studied separately. Additionally, a priori estimates and propositions about nonconstant steady states for the elliptic system are provided. Furthermore, it is discovered that the diffusion rates of susceptible and infected populations can affect the nonexistence of nonconstant steady states. An interesting finding is that the absence of disease-free equilibrium and basic reproduction number occurs when the intrinsic growth rate of susceptible individuals is lower than the rate of vaccination.