A Reaction–Diffusion Model of Vector-Borne Disease with Periodic Delays

A vector-borne disease is caused by a range of pathogens and transmitted to hosts through vectors. To investigate the multiple effects of the spatial heterogeneity, the temperature sensitivity of extrinsic incubation period and intrinsic incubation period, and the seasonality on disease transmission, we propose a nonlocal reaction–diffusion model of vector-borne disease with periodic delays. We introduce the basic reproduction number $$\mathfrak {R}_0$$ for this model and then establish a threshold-type result on its global dynamics in terms of $$\mathfrak {R}_0$$ . In the case where all the coefficients are constants, we also prove the global attractivity of the positive constant steady state when $$\mathfrak {R}_0>1$$ . Numerically, we study the malaria transmission in Maputo Province, Mozambique.