Fig. 5.

Panel a illustrates the basic reproduction number (${\mathcal{R}}_0$) as a function of virulence (${\mu }_S$), considering a transmission rate given by $\beta ({\mu }_S)={\text{sech}}^2(25{\mu }_S-2)$. The plot reveals a global maximum of ${\mathcal{R}}_0$ occurring around ${\mu }_S=0.07$. In panel b, the red curve represents the infected population with the mutant strain (${\mu }_S=0.07$), exhibiting an increasing trend, while the black curve depicts the infected population with the resident strain (${\mu }_S=0.1$), showing a decreasing trend. This observation suggests that the mutant variant is invading the population, indicating that the resident strain is not in its ESS (Color figure online)