A mathematical study unfolding the transmission and control of deadly Nipah virus infection under optimized preventive measures: New insights using fractional calculus

Abstract

This paper presents a new mathematical model governed by a nonlinear fractional-order system of differential equations to investigate the dynamics and optimal control interventions of the Nipah virus using the Caputo derivative. The model describes the effects of inappropriate contact with an infectious corpse as a potential route for virus transmission. We considered two transmission modes while formulating the proposed model: Food-borne transmission and human-to-human transmission. Initially, the model is evaluated with constant controls, and the fundamental analysis is carried out. The model analysis identified three equilibrium states: Nipah virus-free equilibrium, infected flying foxes free equilibrium, and Nipah virus endemic equilibrium state. In addition, a thorough theoretical analysis including stability of the Nipah virus-free equilibrium and Nipah virus endemic equilibrium points of the fractional model is performed. Furthermore, sensitivity analysis of the model parameters is performed to obtain effective time-dependent controls. Based on the sensitivity indices, a fractional optimal control model is presented and the most effective strategy for disease eradication is determined through numerical simulations. The model is optimized using optimal control theory, and Pontryagin’s maximum principle is used to obtain primary optimality conditions. Simulation results are performed to verify the theoretical results.