A mathematical model for non-pharmaceutical interventions in the transmission of COVID-19

Abstract

South Africa is one of the African countries most affected by the Corona pandemic, with total numbers of 1536801 confirmed cases, 1462110 cured cases and 52082 deaths since the onset of the virus until March 20, 2021. This paper aims to provide a mathematical model to predict the transmission dynamics of MERS-CoV and the impact of non-pharmaceutical interventions on disease spread in South Africa using data from May 26, 2020, to March 20, 2021 that cover periods of two epidemic waves. The basic reproduction number (BNR) R₀ and the effective reproduction number R_eff are calculated. Based on the Covid 19 datasets, the model’s parameters are estimated and sensitivity analyses for three parameters of the model that are related to the BNR are carried out, where two of the parameters showed significant effects on the BNR. Numerical simulations of the model are performed using the data of the first and second waves, where the transmissions of MERSCoV in the two waves are compared. The numerical simulations indicates that following nonpharmacological precautions including full or partial lock of the country has a major role in controlling the epidemic and limiting its spread. The model predicts that the infection contact rate is directly proportional to the number of epidemic cases, resulting in the total number of infected cases at the epidemic climax becomes very large. Also, when the closure is implemented earlier and for longer period, it effectively reduces the spread of the epidemic.