A reaction–diffusion model of major emerging infectious diseases in a spatially heterogeneous environment and case study

Abstract

During the outbreak of major emerging infectious diseases, virus droplets can survive in the environment as aerosols for hours to days, and their impact on human infectious diseases is often overlooked. In addition, the speed of transmission of infectious diseases is often closely related to transportation. Therefore, studying the impact of environmental viruses and transportation on disease development is significant for effective infectious disease prevention and control. We proposed a degenerate reaction–diffusion infectious disease model ([Formula: see text]) considering environmental virus interference and established a well-posedness and threshold system for this model. We have obtained the system solution approaches the disease-free equilibrium ([Formula: see text]) when the basic reproduction number [Formula: see text]. The system has at least one positive steady state solution (PSS) when [Formula: see text]. This paper used a non-standard finite difference method discretization model while data fitting and parameter estimation were performed based on data provided by the Health Commission. Further sensitivity analysis was conducted on [Formula: see text]. At the same time, we also discussed the impact of various parameters in the early stages of the outbreak of major emerging infectious diseases on the development of the disease. Research found that even if the contact rate between people is controlled at a shallow level, the disease may persist. In the early stages of major emerging outbreak of infectious diseases, immediately reducing the use of transportation can effectively reduce the speed of disease spread.