International Journal of Science, Engineering and TechnologyAuthors: N.Sreedevi, Daraboina Raj Kumar, Vangala Anjanidevi
Abstract: The increasing threat of emerging and re-emerging infectious diseases in livestock, wildlife, and companion animals demands quantitative frameworks that transcend descriptive epidemiology. Mathematical modeling provides the essential language and toolkit for understanding disease transmission dynamics, predicting outbreak trajectories, and optimizing intervention strategies. This paper synthesizes current advances in three foundational modeling paradigms—compartmental models (SIR-type frameworks), network models, and spatially explicit models—with particular attention to applications published in 2025–2026 across major livestock diseases. We examine how these frameworks have been applied to foot-and-mouth disease, African swine fever, avian influenza, and vector-borne diseases, highlighting methodological innovations in parameter estimation, optimal control theory, and uncertainty quantification. We further identify emerging frontiers, including multiscale models linking within-host to population-level dynamics, machine learning integration for real-time outbreak prediction, and the critical role of sensitivity analysis in identifying key transmission parameters. The synthesis demonstrates that mathematical modeling has moved from retrospective explanation to prospective decision support, providing evidence-based guidance for surveillance, vaccination, culling, and biosecurity policies.
