Spatial and temporal dynamics of COVID-19 with nonlocal dispersal in heterogeneous environment: Modeling, analysis and simulation

Abstract

This paper proposes an infectious disease dynamics model with spatial heterogeneity to study the joint impact of nonlocal dispersal and vaccine on the transmission dynamics of COVID-19 (Corona Virus Disease 2019). Overcoming the difficulty of non-compactness caused by non-local operators, the functional expression of the next generation operator R is obtained by using the renewal equation. And then, the basic reproduction number R0 of the proposed model is obtained, i.e., the spectral radius of the next generation operator R. In terms of theoretical analysis, we prove that the global asymptotic stability of the disease-free steady state when R0<1; Using the uniform persistence theory of point dissipative systems, we prove the system is uniformly persistent and has at least one positive steady state when R0>1. We verify the theoretical results and study the influence of related factors on the transmission of COVID-19 pandemic in numerical simulation part. Finally, our numerical results show that: (1) Improving the coverage rate of COVID-19 complete vaccine and the vaccine efficiency is one of the optimal measures to effectively prevent and control the spread of COVID-19 under the current medical conditions; (2) The influence of the form of nonlocal dispersal kernel function and the virus in environment on the transmission of COVID-19 cannot be ignored Therefore, targeted prevention and control measures should be taken for the dispersal of the virus in urban areas and in the process of cold chain transportation to prevent COVID-19 from spreading to rural areas with relatively backward medical conditions.