Abstract
We consider the transmission of visceral leishmaniasis in three populations: humans, dogs and sandflies. To investigate the effects of spatial heterogeneity and temporal periodicity on disease transmission, a nonlocal periodic reaction‐diffusion equation model is developed. We introduce the basic reproduction number and establish the global dynamics. Numerical simulations show that (i) is overestimated in the absence of spatial heterogeneity; (ii) is underestimated without considering the effect of temporal seasonality; and (iii) shortening periodic delays of visceral leishmaniasis reduces the risk of disease transmission.
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