A Nonlinear Deterministic Model for the Transmission of Influenza A Dynamics

Mathematical models are highly beneficial for analyzing and identifying the most efficient strategies for reducing the severity of epidemics. This work presents and examines a nonlinear deterministic model, designated as SVLIJTR, for the spread pattern of influenza A (H1N1). The model considers the impacts of vaccination and treatment. The fluctuations in the infected population are tracked by evaluating the rates of vaccination, treatment, and isolation. This model rigorously examines the existence and stability of both disease-free and endemic equilibria. The model's basic reproduction number and sensitivity analysis is employed to identify the model parameters that significantly impact . This model is augmented by incorporating an optimal control issue, which includes two types of controls: immunization for susceptible individuals and medical care for those already afflicted. Numerical simulations are employed to evaluate various tactics, concluding that cost-effective analysis is the most efficient approach.