Global dynamics of a reaction-diffusion brucellosis model with spatiotemporal heterogeneity and nonlocal delay

Abstract The increase of animal transportation and livestock lead to repeated outbreaks of brucellosis, and its transmission process is extremely complex. According to the clinical symptoms and infectious differences of the diseased sheep, it is further divided into acute infection and chronic infection, and a reaction-diffusion SLICB (susceptible-latent-acute infected-chronic infected-brucella) model with seasonality, spatial heterogeneity and nonlocal delay is proposed to understand the transmission law of brucellosis and analyze its transmission risk. Based on the basic reproduction number 0 of the model, the final development trend of brucellosis transmission among sheep is analyzed by persistence theory. The 0 of the model is numerically calculated by the generalized power method, and simulation analysis shows that: (i) extending the latent period and increasing the random walk rate of infected sheep can effectively prevent brucellosis from developing into an endemic disease; (ii) the greater the density of acute infections, the higher the risk of brucellosis transmission, and the density of infected sheep and the time to reach the stable state will have a large deviation if only consider acute or chronic sheep; (iii) reaching the peak time will be delayed if the peak time of sheep birth is delayed. These results can provide some suggestions for the control of brucellosis.