Dynamical analysis of a diffusive malaria model with fixed latent period in the human and vector populations

To investigate the impact of the fixed latent periods in the human and vector populations on the disease transmission in heterogenous environment, we formulate a nonlocal and time-delayed reaction-diffusion (NLTD-RD) system. By appealing to the next generation operator (NGO), we define the basic reproduction number (BRN) [Formula: see text], and prove it as a threshold parameter for indicating whether disease persists or not. Specifically, if [Formula: see text], the disease-free equilibrium is globally asymptotically stable, while if [Formula: see text], the disease is shown to be uniformly persistent. In the homogeneous case that all parameters are assumed to be constants, the explicit expression of [Formula: see text] is obtained. We further achieved the global attractivity of the constant equilibria by utilizing Lyapunov functionals. Numerical simulations are performed to verify the theoretical results and the effects of the diffusion rate on disease transmission.