Two mathematical models for H1N1 influenza with antiviral treatment

Abstract

In this paper, we establish two mathematical models to study H1N1 influenza transmission dynamics. One model is for the case of concurrent treatment, in which we assume that untreated individuals are detected at random and moved to the treatment compartment at any time of their infected phase, and the other model deals with the case of early diagnosis, in which we assume that with some probability $\sigma\in[0,1]$, individuals are diagnosed at the moment of infection and immediately moved to the treatment compartment. Both models are analyzed including the derivation of the basic and control reproduction numbers, the proof of global stability of disease-free equilibrium points, and demonstrating how the acquired reproduction number can be used to explain the adverse effects associated with antiviral treatment. This effect is also explained using a quantity termed the total control reproduction number. We also compare the differences between the two models in evaluating outcomes of influenza. Numerical simulations are conducted to verify the theoretical analysis results.