Abstract
A deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals in heterosexual settings in which homosexuality and bisexuality issues have remained taboo is presented. We extend the model to focus on the effects of condom use as a single strategy approach in HIV prevention in the absence of any other intervention strategies. Initially, we model the use of male condoms, followed by incorporating the use of both the female and male condoms. The model includes two primary factors in condom use to control HIV which are condom efficacy and compliance. Reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. We also extend the basic model to consider the effects of antiretroviral therapy as a single strategy. The results from the study show that condoms can reduce the number of secondary infectives and thus can slow the development of the HIV/AIDS epidemic. Further, we note from the study that treatment of AIDS patients may enlarge the epidemic when the treatment drugs are not 100% effective and when treated AIDS patients indulge in risky sexual behaviour. Thus, the treatment with amelioration of AIDS patients should be accompanied with intense public health educational programs, which are capable of changing the attitude of treated AIDS patients towards safe sex. It is also shown from the study that the use of condoms in settings with the treatment may help in reducing the number of secondary infections thus slowing the epidemic.
Highlights
We begin by revisiting a deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of the disease in heterosexual settings in which homosexuality and bisexuality issues have remained taboo, partially studied in [18]
We presented a sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of the disease in heterosexual settings
We extend the model to investigate separately the effects of condom use and antiretroviral therapy on controlling HIV/AIDS in a community
Summary
We begin by revisiting a deterministic compartmental sex-structured HIV/AIDS model for assessing the effects of homosexuals and bisexuals on the intrinsic dynamics of the disease in heterosexual settings in which homosexuality and bisexuality issues have remained taboo, partially studied in [18]. Heterosexual male susceptibles acquire infection at a time-dependent rate lm. In (2), bf is the probability that an infected female infects her male sexual partner, cm is the rate at which heterosexually active male population acquires new sexual partners per unit time and NfðtÞ 1⁄4 SfðtÞ þ IfðtÞ denotes the sexually interacting female population. ; ð3Þ where bh is the probability that an infected homosexual infects his sexual partner, cm is the rate at which heterosexually active homosexual population acquires new sexual partners per unit time and Nm2 ðtÞ 1⁄4 Sm2 ðtÞ þ Im2 ðtÞ denotes the total sexually interacting homosexual population. 0 of individuals to other countries except for the AIDS patients This assumption makes the model more appropriate for African settings (especially Zimbabwe) where a significant proportion of the population emigrates to developed countries for better educational facilities and in search of employment. The partial reproductive number R01 (homosexuality-induced reproductive number) defines the number of secondary infections due to purely homosexual transmission and R02 (heterosexuality and bisexuality-induced reproductive number) defines the number of secondary infections due to heterosexual and bisexual transmission
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