Spatiotemporal Pattern Optimization of SI Model Based on PD Control Strategy

Current research on the spatial patterns of epidemic models, both domestically and internationally, tends to focus on the impact of system parameters or diffusion coefficients on these patterns. However, studies on controlling these spatial patterns are relatively scarce. Effective control of spatial patterns in epidemic models can be crucial for predicting epidemic dynamics within specific areas. This article establishes an SI spatial epidemic model incorporating self-diffusion and cross-diffusion terms. A proportional differential controller is proposed to manage the spatial patterns of the SI model. Conditions are also provided under which the controlled system experiences Hiring instability. The effectiveness of the controller is validated through numerical simulations.