Author(s): Patrick Muriuki Kamuri, Cyrus Gitonga Ngari, Peter Wanjohi Njori and Jeremiah Savali Kilonzi

Abstract: Homosexuality has become a global trend both in developing and developed countries. While it has been legalized in some countries, it’s still illegal in others. In this paper, a comprehensive mathematical model of sexual orientations with recovery centers was developed using a set of ordinary differential equations and solved using Wolfram Mathematica and the fourth-order Runge-Kutta method. The population was divided into ten compartments; Males (M), Females (F), gays (G), lesbians (L), heterosexual males (H_m), heterosexual females (H_f), bisexual males (B_m), bisexual females (B_f), recovery centers for males (R_m) and recovery centers for females (R_f). Positivity, boundedness, the homosexuality epidemic threshold, and equilibria for the model were determined, and stabilities were investigated. Moreover, control reproduction number and bifurcation analysis were also studied. The sensitivity of the parameters was investigated using the partial rank correlation coefficient (PRCC) method and Latin hypercube sampling (LHS). Numerical simulation was done using MATLAB 45-ODE Solver and showed that increasing homosexuality recruitment rates increased homosexuality in the population, and vice versa. It was also established numerically that increasing transfer rates from the bisexual classes to recovery centers increased the heterosexual populations. In conclusion, the effective transfer to recovery centers of the homosexual populations and low contact rates are most significant in reducing the spread of homosexuality in the community.

DOI: 10.22271/maths.2025.v10.i6a.2053

Pages: 18-28 | Views: 926 | Downloads: 18

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