Spatiotemporal Analysis of Disease Spread Using a Soliton-Based SIR Framework for Nomadic Populations

This study enhances the classical deterministic SIR model by incorporating soliton-like dynamics and gradient-induced diffusion, effectively capturing the complex spatiotemporal patterns of disease transmission within nomadic populations. The proposed model incorporates an advection–diffusion mechanism that modulates the spatial gradients in infection dynamics, transitioning from highly localized infection peaks to distributed infection fronts. We discussed the role of diffusion coefficients in shaping the spatial distribution of susceptible, infected, and recovered populations, as well as the impact of gradient-induced advection in mitigating epidemic intensity. Numerical simulations demonstrate the effects of varying key parameters such as transmission rates, recovery rates, and advection–diffusion coefficients on the epidemic’s progression. The soliton-like dynamics ensure the stability of infection waves over time, specifying targeted intervention strategies such as localized quarantines and vaccination campaigns. This model underscores the critical importance of spatial heterogeneity and mobility patterns in managing infectious diseases. The applicability of the model has been tested using the AIDS data from the last 25 years.