Predator-prey model of HIV propagation in a heterosexual community

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The objective of this project is to apply the predator –prey model to come out with a model for the propagation of HIV, taking into consideration the population of newly infected males and newly infected females at a given time. This particular model is conjectured because it has been observed that there is an almost sinusoidal rising and falling of the time series trajectories of newly infected male and female cases of the Ghana data. With some few assumptions made the model is formulated and the analysis shows that it conforms to the predator – prey model. Even though parameters in respect of newly infected males and females were not directly available for the simulation, with some assumptions, the parameters of the model are estimated and the simulation of the model for various scenarios using MATLAB is done. These simulations give the typical almost sinusoidal trajectories for both the populations of the newly infected males and newly infected females. This appears to confirm that the propagation of HIV follows the predator – prey model. It also shows that the rate of infections of HIV keeps rising and falling with time. The curves also show that more females are infected at any given time than males. Some recommendations regarding the eradication of HIV or the curtailment of the spread of HIV are offered.
A Thesis Submitted to the Department of Mathematics in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Philosophy in Mathematics