Mathematical model of sexual orientations with advocacy

Abstract

Sexual orientation is the attraction one feels to men, women, or both, while advocacy is any effort or activity geared towards supporting people of diverse sexual orientations to eradicate discrimination within a community. In this paper, a comprehensive mathematical model of sexual orientations with advocacy was developed, and the efficacy of advocacy is analysed. The model divided the population into ten compartments: Males, Females, gays, lesbians, heterosexual males, heterosexual females, bisexual males, bisexual females, recovery centres for males, and recovery centres for females. The

positivity, boundedness, equilibria points, and control reproduction numbers were studied. The Routh- Hurwitz criteria were used to assess the local stability of the disease-free equilibrium, the Metzler Matrix

method was used to determine global stability, while Lyapunov functions were used to study the global stability of the endemic equilibrium point. Bifurcation analysis was also conducted. Lastly, a sensitivity analysis and numerical simulations were conducted using Wolfram Mathematica and MATLAB software. Numerical results showed that the model with advocacy increases the gay, lesbian, bisexual male, and bisexual female populations by 5.7%, 15.6%, 2.6%, and 15.3%, respectively, compared with the model without advocacy. In conclusion, the study showed that while incorporating advocacy in the community significantly increased homosexual populations in the society, Lesbian and bisexual female populations were increased the most.