# Bifurcations and optimal control in Nipah virus epidemiology

## TL;DR

This paper develops a mathematical model to study Nipah virus spread and optimal control strategies to reduce its impact.

## Contribution

A novel six-compartment model with waning immunity and optimal control analysis for Nipah virus epidemiology.

## Key findings

- The model confirms a forward bifurcation at the epidemic threshold.
- Optimal control strategies significantly reduce infection burden and costs.
- Combined interventions can minimize final epidemic size and increase immunity.

## Abstract

Nipah virus (NiV) is a zoonotic pathogen with a high case fatality rate, posing a significant and ongoing threat to public health in Asia. This study develops a comprehensive mathematical framework to analyze its transmission dynamics and evaluate effective control strategies. We introduce a novel six-compartment model (SEAIHR) that stratifies the population into Susceptible, Exposed, Asymptomatic, Symptomatic Infected, Hospitalized, and Recovered individuals, incorporating key features such as waning immunity. Analytical results determine the basic reproduction number and establish the global stability of both the disease-free and disease equilibria, confirming a forward bifurcation at the epidemic threshold. A sensitivity analysis identifies the recruitment rate and the disease transmission rate as the most influential parameters on outbreak potential. Furthermore, we formulate an optimal control problem to evaluate the impact of three time-dependent intervention measures: public health campaigns to reduce contact, isolation of symptomatic individuals, and improved treatment for hospitalized patients. The optimal strategies derived from Pontryagin’s Maximum Principle demonstrate a significant reduction in the overall infection burden and intervention costs. Numerical simulations validate the model and show that these combined controls can effectively minimize the final epidemic size while increasing the population’s immunity. This work provides a quantitative framework to guide the design of efficient public health policies for managing and mitigating Nipah virus outbreaks.