A Model Analysis for the Transmission Dynamics of Avian Influenza

This paper examines the transmission dynamics of avian influenza. A nonlinear mathematical model for the problem is formulated and analysed. For the prevalence of the disease and the ease of analysis, we considered the model in proportions of susceptible, infectious, isolated and recovered compartments. The basic reproduction number was computed and used to prove the stability of the disease free equilibrium states. It is proved that the basic reproduction number is a decreasing function of the culling rate of infected birds. It is further proved that the disease free equilibrium state is locally asymptotically stable whenever the basic reproduction number is less than unity. Key words: Avian influenza, Mathematical model, Basic reproduction number. Disease free equilibriu

Numerical Simulation for the Transmission Dynamics of Avian Influenza

This paper presents numerical simulations for the transmission dynamics of avian influenza using the model formulated and analysed by Kimbir etal (2014). It is proved that the disease free equilibrium state is locally asymptotically stable whenever the reproduction number is less than unity. The implication is that if the reproduction number is less than unity, the infection is controlled or eradicated and the disease persists otherwise. The numerical simulations are consistent with the local stability of the disease-free states. The simulations further reveals that the infection transmission rate constitutes an essential parameter for an epidemic to occur, thus efforts should be geared at bringing the infection transmission to the lowest level in order to ensure eradication. It was also shown from the study that increasing culling of infected birds, will reduce the disease progression within the birds’ population thereby, reducing the transmission of avian influenza. Effective isolation of infected individuals without culling is vital to eradicating the disease transmission, but a combined effective use of culling of infected birds and isolation of infected humans is a strong control measure against pandemics. Key words: Avian influenza, Mathematical model, Basic reproduction number, Numerical simulation

Existence and Uniqueness of Solution of an HIV/AIDS Model Considering Counseling, Vaccination and Antiretroviral Therapy (ART)

The control of HIV/AIDS is not yet over. Recently, the main method of control is the use of counseling and antiretroviral therapy (ART). In this study, a mathematical model of HIV/AIDS transmission dynamics considering counseling, vaccination and ART is formulated and the existence of its unique solution is investigated.Key words: HIV/AIDS, Mathematical Model, Existence and Uniqueness of Solution, Counselling, Vaccination, Antiretroviral Therap