| Abstract: |
| Mathematical modeling has played a key role in understanding the spread of COVID-19 and guiding public health interventions. While the effects of medical masks and reinfection have been widely studied, their interaction remains less explored. In particular, how mask usage influences reinfection dynamics can significantly alter disease outcomes but is often overlooked. In this study, we develop a transmission model that incorporates medical mask usage, reinfection, and treatment limitations. Our analysis shows that even when the basic reproduction number $\mathcal{R}_0$ is below one, the disease may still persist due to complex system behavior. This highlights that controlling COVID-19 is not always as straightforward as reducing $\mathcal{R}_0$. Through detailed numerical analysis, we uncover rich dynamics such as oscillatory outbreaks and multiple endemic states, which may explain recurring waves of infection observed in real-world data. Our results demonstrate that reinfection can fundamentally change disease dynamics, while consistent mask usage remains a crucial intervention. These findings suggest that adaptive and sustained strategies are necessary to prevent repeated outbreaks. Beyond COVID-19, this work emphasizes how combining behavioral and epidemiological factors in mathematical models can provide deeper insights for designing effective public health policies. |
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