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.
Highlights
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
The paper [12] gives a new idea about acquired reproduction number, which can be used to explain the adverse effects associated with antiviral treatment
We denote the sum of components 3, 4 and 5 by RAR, which refers to the acquired reproduction number and can be used to explain the adverse effects associated with antiviral treatment
Summary
Influenza ( known as flu) is a respiratory disease caused by certain RNA viruses of the Orthomyxoviridae family [1]. The government of China took a series of emergency measures, such as setting up work mechanism to prevent H1N1 influenza from spreading; adopting strict inspection and quarantine measures in the ports of entry and exit; strengthening the management of close contacts; monitoring and reporting infected individuals; and constantly adjusting and improving the diagnosis and treatment of cases. One of such strategies is treatment of affected patients with antiviral medication.
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