Optimal control analysis for the Nipah infection with constant and time-varying vaccination and treatment under real data application.

In the last two decades, Nipah virus (NiV) has emerged as a significant paramyxovirus transmitted by bats, causing severe respiratory illness and encephalitis in humans. NiV has been included in the World Health Organization's Blueprint list of priority pathogens due its potential for human-to-human transmission and zoonotic characteristics. In this paper, a mathematical model is formulated to analyze the dynamics and optimal control of NiV. In formulation of the model we consider two modes of transmission: human-to-human and food-borne. Further, the impact of contact with an infected corpse as a potential route for virus transmission is also consider in the model. The analysis identifies the model with constant controls has three equilibrium states: the NiV-free equilibrium, the infected flying foxes-free equilibrium, and the NiV-endemic equilibrium state. Furthermore, a theoretical analysis is conducted to presents the stability of the model equilibria. The model fitting to the reported cases in Bangladesh from 2001 to 2015, and the estimation of parameters are performed using the standard least squares technique. Sensitivity analysis of the model-embedded parameters is provided to set the optimal time-dependent controls for the disease eradication. The necessary optimality conditions are derived using Pontryagin's maximum principle. Finally, numerical simulation is performed to determine the most effective strategy for disease eradication and to confirm the theoretical results.