Threshold dynamics of a time-delayed dengue virus infection model incorporating vaccination failure and exposed mosquitoes

A time-delayed dengue virus transmission model has been developed, which takes into account vaccination failure and the presence of exposed mosquitoes. This model also incorporates the survival probability of infected individuals during the incubation period to provide a clearer understanding of how latency affects the control reproduction number $R_c$. Furthermore, by employing the Lyapunov functional approach, we establish the global asymptotic stability of equilibria in relation to $R_c$. The results indicate that the disease-free equilibrium $T^0$ is globally asymptotically stable if and only if $R_c\le 1$, whereas the endemic equilibrium $T^{\ast }$ is globally asymptotically stable if and only if $R_c>1$.