A reaction-diffusion vector-borne disease model with incubation period in almost periodic environments (Q6577353)

To examine the impact of the incubation period on vector-borne disease transmission, this paper proposed and analyzed a nonlocal almost periodic reaction-diffusion model for vector-borne diseases. First, the authors provided a characterization of the upper Lyapunov exponent \( \lambda^* \) for a class of linear almost periodic reaction-diffusion systems with time delay and present a numerical scheme for computing it. They demonstrate that \( \lambda^* \) acts as a threshold value, determining the model's uniform persistence or extinction behavior: the disease will fade out if \( \lambda^* < 0 \), while it will persist uniformly if \( \lambda^* > 0 \). Finally, numerical simulations are provided to validate our theoretical results and explore the effects of diffusion rates, the extrinsic incubation period, and spatial heterogeneity on disease transmission.