Continuous time stochastic model for the COVID-19 pandemic in Nigeria

The rapid surge in cases of the novel coronavirus disease (COVID-19), caused by the new strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), remains a critical health concern in Nigeria and a global challenge. In this study, we propose an epidemic SVEnEpIQR model that incorporates the behavior of exposed individuals towards COVID-19 protocols and guidelines, as well as the effectiveness of quarantine and vaccination measures. Our model employs a Continuous Time Birth and Death process, presenting transition probabilities, establishing the Kolmogorov master equation, and utilizing the probability generating function approach to derive the expectation equation for each compartment. We conducted stochastic simulations and visualizations for each compartment, and the results align with epidemic response patterns observed in other models that rely on detailed population-level data. The predicted epidemic curve closely resembles the actual situation in Nigeria. Our findings indicate that an increase in the transmission intensity, quarantine and recovery rates leads to a rise in the number of secondary cases of infection. Moreover, we discovered that relying solely on quarantine and treatment of active COVID-19 cases will reduce the number of infected individuals but not the duration of virus spread. Importantly, we conclude that an increased vaccination rate among susceptible individuals not only reduces the number of infected individuals but also curtails the duration of the COVID-19 pandemic in Nigeria.

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