ABSTRACT During the process of disease transmission, indirect infections caused by pathogens in the environment are often overlooked. Even a small amount of virus surviving in the environment can cause the rapid spread of the disease. Furthermore, memory‐dependent movement is a key feature of individual movement strategies. This paper investigates a spatially heterogeneous epidemic model that couples direct and indirect transmission with the memory‐dependent movement of susceptible individuals. The memory effect is modeled through a spatiotemporal convolution term that biases susceptible movement away from past infection landscapes. We prove the wellposedness of our models and establish the precompactness of the solution semiflow. Through the next generation operator, we define the basic reproduction number and obtain the threshold dynamics: The system is uniformly persistent when ; the disease‐free steady state is globally attractive when . Numerically, we show that the memory‐dependent movement of susceptible individuals alters the early dynamics of disease transmission but does not eradicate the disease. Moreover, we show that direct transmission ultimately dominates disease transmission, although indirect transmission is also significant during certain periods. Motivated by the dependence of pathogen decay on environmental conditions, we incorporate temperature and relative humidity into the decay rate and quantify the impact of these factors on disease transmission.
Lu et al. (Wed,) studied this question.