📂Dynamics

Sexually Transmitted Diseases Model: Disease Transmission between Two Populations

Overview

Cooke and Yorke’s proposed mathematical model for the spread of sexually transmitted diseases is explored. In references, gonorrhea is considered as a specific example of a sexually transmitted disease.

Model ¹

$$ \begin{align*} {{d S_{1}} \over {d t}} =& - \beta_{12} S_{1} I_{2} + \gamma_{1} I_{1} \\ {{d I_{1}} \over {d t}} =& \beta_{12} S_{1} I_{2} - \gamma_{1} I_{1} \\ {{d S_{2}} \over {d t}} =& - \beta_{21} S_{2} I_{1} + \gamma_{2} I_{2} \\ {{d I_{2}} \over {d t}} =& \beta_{21} S_{2} I_{1} - \gamma_{2} I_{2} \end{align*} $$

Variables

• $S_{k}(t)$: Represents the number of individuals in the $k$-th group that are susceptible to the disease at time $t$.
• $I_{k}(t)$: Represents the number of individuals in the $k$-th group that can transmit the disease at time $t$. In the context of information dissemination, it also follows the initial letter of Informed.

Parameters

• $\beta_{ij}>0$: The infection rate from group $i$ to group $j$.
• $\gamma_{k}>0$: The recovery rate of group $k$.

Explanation

Essentially, it uses the SIS model, but regardless of that, the key point is that the entire population is divided into two groups $k=1,2$. Naturally, this index represents the distinction between men and women, and considering the real-world dating market, $\beta_{12}, \beta_{21}$ should be significantly different values.