| Abstract: |
| In this talk, I will present a non-autonomous mathematical model that explore the complex dynamics of disease spread over time, incorporating a time-periodic transmission parameter and imperfections in quarantine, isolation and vaccination strategies. Through a detailed examination of threshold dynamics, it is revealed that the global dynamics of disease transmission are influenced by the basic reproduction number ($\mathcal{R}_0$), a critical threshold that determines extinction, persistence, and the presence of periodic solutions. It is shown that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0 1$. To support and validate our analytical results, the basic reproduction number and the dynamics of the disease are estimated by fitting monthly data from two Asian countries, namely Saudi Arabia and Pakistan. Furthermore, a sensitivity analysis of the time-averaged reproduction number ($\langle \mathcal{R}_0 \rangle$) of the associated time-varying model showed a significant sensitivity to key parameters such as infection rates, quarantine rate, vaccine coverage rate, and recovery rates, supported by numerical simulations. These simulations validate theoretical findings and explore the impact of seasonal contact rate, imperfect quarantine, isolation, imperfect vaccination, and other parameters on the dynamics of measles transmission. The results show that increasing the rate of immunization, improving vaccine management, and raising public awareness can reduce the incidence of the epidemic. The study highlights the importance of understanding these patterns to prevent future periodic epidemics. |
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