Modeling the multi-species spread of nipah virus via a spatial reaction-diffusion framework

This study develops and analyzes a spatially explicit mathematical model for the transmission dynamics of the Nipah virus among human, livestock (farmers), and bat populations using a system of nonlinear reaction-diffusion partial differential equations. The model incorporates interspecies transmission pathways, demographic processes, and spatial diffusion to capture realistic host movement and disease propagation. We derive the disease-free equilibrium (DFE) and rigorously compute the basic reproduction number R0 using the next-generation operator approach in the PDE context. Analytical results establish that the DFE is globally asymptotically stable when R0<1, ensuring eventual disease eradication under sub-threshold conditions. Conversely, for R0>1, the system admits an endemic equilibrium, potentially spatially heterogeneous, whose existence is supported analytically and confirmed through numerical simulations. To solve the model efficiently, we propose a computationally efficient Crank–Nicolson Operator Splitting Finite Difference (CNOS-FD) algorithm that decouples reaction and diffusion processes, preserving numerical stability and accuracy. A variety of initial conditions, including Gaussian and multiple-Gaussian spatial distributions, are employed to evaluate the model’s dynamic response. Sensitivity analysis based on Latin Hypercube Sampling and Partial Rank Correlation Coefficients identifies the most influential parameters driving R0 and disease persistence, offering insights into effective intervention strategies. Numerical experiments illustrate the emergence of spatial patterns, infection wavefronts, and long-term persistence scenarios, highlighting the critical role of diffusion and local transmission in shaping epidemic outcomes. This framework offers a robust platform for spatial epidemic forecasting and underscores the importance of spatially targeted control measures in mitigating Nipah virus outbreaks.