Transmission dynamics of visceral leishmaniasis with PKDL and periodic delays.

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 R0$$ {\mathcal{R}}_0 $$ and establish the global dynamics. Numerical simulations show that (i) R0$$ {\mathcal{R}}_0 $$ is overestimated in the absence of spatial heterogeneity; (ii) R0$$ {\mathcal{R}}_0 $$ is underestimated without considering the effect of temporal seasonality; and (iii) shortening periodic delays of visceral leishmaniasis reduces the risk of disease transmission. [ABSTRACT FROM AUTHOR]