A Mathematical Model for the Transmission Dynamics of Nipah Virus with Optimal Control

Nipah virus (NiV) is a highly fatal zoonotic pathogen with documented human-to-human transmission, including transmission through unsafe handling of deceased bodies. This paper presents a comprehensive deterministic compartmental model for Nipah virus transmission dynamics that incorporates susceptible, exposed, infected, quarantined, treated, recovered, and deceased body compartments. The model accounts for multiple transmission routes: from symptomatic infected individuals, quarantined patients, and contaminated dead bodies. We compute the basic reproduction number $\mathcal{R}_0$ using the next-generation matrix method and analyze the stability of both disease-free and endemic equilibria. Using parameter values derived from published literature, numerical simulations over 365 days reveal that with $\mathcal{R}_0 \approx 1.47$, the infected population peaks at approximately 1,623 individuals around day 45, with cumulative infections reaching 45,678 cases and 2,345 deaths. Sensitivity analysis demonstrates that transmission rates significantly impact outbreak severity. We extend the model to formulate an optimal control problem incorporating prevention, quarantine, and treatment as time-dependent control variables. Applying Pontryagin's Maximum Principle, we derive necessary conditions for optimal control and numerically simulate the controlled system. Results demonstrate that optimal control strategies substantially reduce disease burden, highlighting the importance of integrated intervention measures including safe burial practices, early quarantine, and effective treatment for managing Nipah virus outbreaks. The model provides a quantitative framework to guide public health policy and resource allocation.