Problems of Automated Control of Viral Disease Progression Accounting for Spatial Perturbations and Body Temperature Response Under Immunotherapy

We develop a spatiotemporal mathematical model describing viral infection dynamics under the combined effects of diffusion, convection, temperature-dependent immune response, and therapeutic intervention. The model is formulated as a system of singularly perturbed delay partial differential equations that captures the interactions among viral particles, immune agents, target-organ damage, and body-temperature regulation. To efficiently compute approximate solutions, we propose a hybrid asymptotic–numerical framework that combines the method of steps with singular perturbation techniques. The delayed system is transformed into a sequence of auxiliary non-delay problems, allowing the systematic construction of computationally efficient approximations while preserving the essential multiscale characteristics of the original model. An adaptive control strategy is introduced to regulate immunological and antipyretic therapies based on predicted system evolution. Numerical experiments are performed to investigate the effects of treatment timing, dosage, and temperature regulation on infection progression. The simulations demonstrate that early therapeutic intervention improves viral suppression, whereas excessive temperature reduction may diminish the protective effects of the febrile response and lead to less favorable outcomes. The proposed framework provides an efficient computational tool for the analysis and control of spatially distributed infection dynamics and represents a step toward the development of personalized treatment strategies based on predictive mathematical modeling.