Mathematical Model of COVID-19 Spread with Vaccination  in Mataram City

Muhammad Putra Sani Hattamurrahman; Paian Sianturi; Hadi Sumarno

doi:10.31764/jtam.v8i4.23113

Mathematical Model of COVID-19 Spread with Vaccination in Mataram City

Muhammad Putra Sani Hattamurrahman, Paian Sianturi, Hadi Sumarno

Abstract

The COVID-19 pandemic has had a significant impact on public health worldwide.. Mathematical modeling is considered an alternative tool for understanding real-life problems, including the dynamics of COVID-19 spread. This is an applied research that purpose adds vaccination to Zeb et al. (2020) SEIQR model of COVID-19 spread and examines the dynamic of COVID-19 spread in Mataram City. First, we construct the new model by making assumptions. The fixed point and basic reproduction number (R_0 ) are then used to analyze the model using the next-generation matrix method. The next-generation matrix method is utilized to estimate the R_0 in a compartmental disease model. Two fixed points are acquired, specifically the disease-free fixed point, which is locally asymptotically stable under the condition R_0<1 determined by the Routh Hurwitz criterion via linearization using the Jacobi matrix. And the disease-endemic fixed point, which is locally asymptotically stable under the condition R_0>1 indicated by Lyapunov function. The population dynamics when R_0<1 and R_0>1 can also be observed through numerical simulation. The results of a numerical simulation indicate that giving the proportion of number vaccinated 62 per cent is effective in suppressing the number of infections.

Keywords

COVID-19; Vaccination; Mathematical model; Basic reproduction number; Routh Hurwitz criterion; Lyapunov function; Mathematical model.

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DOI: https://doi.org/10.31764/jtam.v8i4.23113