In this paper, a non-linear mathematical model was proposed to study the combined effect of irresponsible infectives and irresponsible susceptible immigrants on the spread of human immunodeficiency virus/acquired immune deficiency syndrome (HIV/AIDS) in a variable size population. The paper discussed biological feasibility of the model and also presents the basic reproductive number of the model. Also, the equilibrium points of the model are found and stability of the model around the equilibria was also studied. It is realized that at the disease free equilibrium, the model is stable when R0 < 0 and unstable otherwise. Also, the condition for asymptotical stability of the model near the endemic equilibrium is presented. The equilibra of model is given as. Numerical simulations reveal that the presence of infective immigrants significantly affects the spread of the disease and that behavioral change of all classes of individuals should be considered in efforts aimed at controlling the spread of the disease.
Key words: Acquired immune deficiency syndrome (AIDS) epidemic, vertical transmission, stability, infective immigrants, simulation.
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