Transmission and Control Dynamic Model of Influenza Virus Infection

Influenza virus infection is one of the diseases that pose a global threat and causes seasonal outbreaks and pandemics. As a result, it is associated with a high rate morbidity and mortality worldwide despite the availability of vaccine and antiviral drugs. To understand the transmission and control dynamics of this threatening infection, we formulated a six compartmental mathematical model, which incorporated vaccination and treatment parameters into the deterministic model that studies the behaviour of the infection. The mathematical analysis shows that the disease free and the endemic equilibrium point of the model exist. The model has disease free equilibrium point which is both locally and globally asymptotically stable whenever the basic reproduction number is less than unity (i. e. when and unstable when. In the same way, the endemic equilibrium is also locally asymptotically stable. Numerical simulation was carried out by Maple 18 software using differential transformation method to investigate the effects of vaccine, recovery (due to body immunity), and treatment on the dynamics of the disease. Our results showed that increasing the rates of vaccination and recovery has a significant effect of reducing infection in both populations of the infected individuals and increases the recovered and susceptible populations. However, although treatment decreases infection in the symptomatic infected population, it has a negative effect of increasing infection among the asymptomatic infected individuals. This effect can be reversed by screening all individuals to know their infection status so that necessary measure will be taken. Also, our result show that vaccine wanes off after some time and so, it was recommended that influenza vaccines be taken periodically (annually, biennially or otherwise, depending on the expiry duration) for renewal sake in order to lower the rate at which vaccine wanes off.