Fractional modeling of zoonotic spillover with optimal control in a multi host system
Résumé
Abstract We propose a fractional-order multi-host epidemic model that captures zoonotic spillover dynamics across human, pig, and bird populations. The model is formulated using the Caputo fractional derivative to incorporate memory effects arising from past infection states, which are not accounted for in classical integer-order models. The transmission structure explicitly represents cross-species pathways, including bird-to-pig, pig-to-human, and within-host transmission dynamics, providing a realistic framework for multi-host disease spread. Although the model is general, it is motivated by zoonotic systems such as Nipah virus, where such transmission routes are epidemiologically relevant. Unlike existing studies, this work simultaneously integrates fractional dynamics, multi-host coupling, and time-dependent optimal control strategies, thereby extending both classical epidemic models and recent fractional-order formulations. Numerical simulations show that reducing the fractional order significantly lowers peak infection levels (by more than 40% in some scenarios) and delays epidemic peaks, while optimal control further drives the system toward disease-free equilibrium. Additionally, contour and phase-portrait analyses illustrate how coordinated interventions reshape the basic reproduction number landscape and redirect system trajectories toward elimination. These findings provide new insights into the role of memory and control in shaping the dynamics of complex zoonotic diseases.
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