Modeling HIV In The Presence Of Infected Immigrants And Vertical Transmission: The Role Of Incidence Function
Ochoche, Jeffrey M.
Keywords: Basic Reproduction number, Epidemiology, HIV, Incidence function, Infected immigrants, Stability, Vertical transmission
Abstract: We formulated three mathematical models for the transmission dynamics of HIV in the presence of infected immigrants and vertical transmission using a deterministic approach. Three forms of incidences popularly used in epidemiology were considered: The mass action, Standard and non-linear/saturated incidences. A Basic Reproduction number was derived for each model and used to prove its local stability. All the models were found to be globally asymptotically stable at the disease-free equilibrium. The mass action incidence and the non - linear incidence yielded similar analytical results e.g their Basic Reproduction numbers are identical and greater than the Basic Reproduction number of the Standard incidence model. Further, only the numerical simulation of the standard incidence model was biologically meaningful and we concluded that for sexually transmitted diseases the standard incidence is most appropriate.
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