Modeling and optimal control analysis of influenza model

Influenza Model

Abstract

Influenza is a respiratory infectious disease caused by the influenza virus, which is commonly known as the flu. In this paper, a deterministic model of influenza is proposed and investigates the impact of optimal control strategies with treatment function. The disease-free equilibrium point and the basic reproduction number $\mathcal R_0$ of the model are computed. The sensitivity analysis is performed to identify the key parameters that affect the basic reproduction number, which can be regulated to control the transmission dynamics of the influenza. To investigate the optimal control strategies, three types of time-dependent control parameters are introduced in the system to reduce the transmission. We investigated the appropriate optimal control strategies to eradicate the transmission of the disease. Pontryagin's maximum principle is used to manifest the optimal control strategies. It is noticed that the optimal control model gives better results than the model without optimal control. Further with the help of numerical simulations, the theoretical results are compared.