Mathematical Modeling of Influenza Transmission Dynamics with Immigration and Control Strategy

Abstract

This paper developed a mathematical model to investigate the transmission dynamics of influenza fever with vaccination and quarantine as control strategies. In developing our model, the population was compartmentalized into susceptible-vaccinated-exposed-infected-quarantine-recovered (SVEIQR) and allowed immigrations into susceptible and exposed compartment only. The model developed in a system of differential equations. Equilibrium points of the system and basic reproduction number were obtained, existence and uniqueness of the solution, invariant region, positivity of the solution was established and we also carryout local and global stability analysis of disease free equilibrium state. Linearization method was used for proving the local stability of equilibrium while Carlo Castillo-Chavez method was adopted for proving the global stability of the equilibrium points. Analytical solution shows that, the dynamics of spread of the influenza fever is determined by the basic reproduction number if < 1, the influenza free equilibrium is locally asymptotically stable or otherwise, if > 1. In this regard, Government and non-governmental organization of every country should encourage the use of influenza vaccine among individuals.