In this paper, we develop a mathematical model describing the dynamics of HIV transmission by incorporating sexual orientation of individuals. Equilibrium points and the basic reproduction number are derived. The basic reproduction number provides a threshold that determines whether or not the disease fades away. The model, described by non-linear ODEs, shows existence of unique diseasefree and disease-persistent equilibria. Least squares curve fitting is presented to quantitatively investigate the trend of infection within each gender. The results are indicative of a higher infectivity in the female population. We further investigated the effect of the introduction of pre-exposure prophylaxis (PrEP) on the dynamics of the HIV. Our results show that the introduction of PrEP has had a positive effect on the limitation of spread of HIV. Sensitivity analysis results show that control of effective contacts can result in control of the disease across gender divide. The model provides a unique opportunity to influence policy on HIV treatment and management.
The control of HIV demands different interventions for different age groups. In the present manuscript, we formulate and analyze a mathematical compartmental models of HIV transmission within and between two age groups in Kenya. We fitted the model to data using MCMC technique and inferred the parameters. We also estimate the reproduction numbers, namely within age group transmission and between age groups transmission basic reproduction numbers. The analysis of the data revealed that there is significant difference in mean number of new HIV infections between males and females within the two age groups. More, particularly, females are highly infected with HIV as compared to their male counterparts. Calculation of the reproduction numbers within and between age groups provides insights into control that cannot be deduced simply from observations on the prevalence of infection. More specifically, the analysis showed that the per capita rate of HIV transmission was highest when there is interaction between young adults to adults and most HIV infections occurred in adult population. Furthermore, the sensitivity analysis demonstrated that the reproduction numbers depend mainly on the probabilities of infection. This results can be used to guide HIV interventions, condom distribution and antiretroviral therapy. Precisely, the results can be used to educate the young adults on practicing safe sex with their partners in order to contain the occurrence of new infections.
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