Pattern formation of parasite-host model induced by fear effect

In this paper, based on the epidemiological microparasite model, a parasite-host model is established by considering the fear effect of susceptible individuals on infectors. We explored the pattern formation with the help of numerical simulation, and analyzed the effects of fear effect, infected host mortality, population diffusion rate and reducing reproduction ability of infected hosts on population activities in different degrees. Theoretically, we give the general conditions for the stability of the model under non-diffusion and considering the Turing instability caused by diffusion. Our results indicate how fear affects the distribution of the uninfected and infected hosts in the habitat and quantify the influence of the fear factor on the spatiotemporal pattern of the population. In addition, we analyze the influence of natural death rate, reproduction ability of infected hosts, and diffusion level of uninfected (infected) hosts on the spatiotemporal pattern, respectively. The results present that the growth of pattern induced by intensified fear effect follows the certain rule: cold spots $\rightarrow$ cold spots-stripes $\rightarrow$ cold stripes $\rightarrow$ hot stripes $\rightarrow$ hot spots-stripes $\rightarrow$ hot spots. Interestingly, the natural mortality and fear effect take the opposite effect on the growth order of the pattern. From the perspective of biological significance, we find that the degree of fear effect can reshape the distribution of population to meet the previous rule.