Assessment of the Impacts of Pharmaceutical and Non-pharmaceutical Intervention on COVID-19 in South Africa Using Mathematical Model

Abstract

The novel coronal virus has spread across more than 213 countries within the space of six months causing devastating public health hazard and monumental economic loss. In the absence of clinically approved pharmaceutical intervention, attentions are shifted to non-pharmaceutical controls to mitigate the burden of the novel pandemic. In this regard, a ten mutually exclusive compartmental mathematical model is developed to investigate possible effects of both pharmaceutical and non-pharmaceutical controls incorporating both private and government’s quarantine and treatments. Several reproduction numbers were calculated and used to determine the impact of both control measures as well as projected benefits of social distancing, treatments and vaccination. We investigate and compare the possible impact of social distancing incorporating different levels of vaccination, with vaccination programme incorporating different levels of treatment. Using the officially published South African COVID-19 data, the numerical simulation shows that the community reproduction threshold will be 30 when there is no social distancing but will drastically reduced to 5 (about 83% reduction) when social distancing is enforced. Furthermore, when there is vaccination with perfect efficacy, the community reproduction threshold will be 4 which increases to 12 (about 67% increment) with-out vaccination. We also established that the implementation of both interventions is enough to curtail the spread of COVID-19 pandemic in South Africa which is in confirmation with the recommendation of the world health organization.

Assessing the impact of non-pharmaceutical interventions (NPI) on the dynamics of COVID-19: A mathematical modelling study of the case of Ethiopia

“…[ 47 ] estimated the COVID-19 case burden for all African countries under different intervention scenarios (no intervention, moderate lock-down and hard lock-down) using a compartmental model. [ 48 ] studies the impacts of pharmaceutical and non-pharmaceutical interventions on COVID-19 in South Africa using a mathematical model and additionally, proper implementation of physical distancing greatly reduced the basic reproduction number.…”

Assessing the potential impact of immunity waning on the dynamics of COVID-19: an endemic model of COVID-19

“…The disease-free equilibrium of (2.2)-(2.7) is given by where . We calculate the control reproduction number using the next generation matrix operator [13, 59] on (2.2)-(2.7) as used by [46, 51]. The matrix for the rates of new infections ℱ and that of transfer of infected individuals, 𝒱 at the DFE are given by …”

“…Several mathematical models have been developed and analyzed to study the transmission dynamics of COVID-19 [2, 4, 26, 27, 33, 53, 39, 46, 66, 70]. Bugalia et al [4] developed a COVID-19 model using an endemic framework considering the roles of intervention strategies such as lockdown, hospitalization and quarantine.…”

Assessing the Potential Impact of Immunity Waning on the Dynamics of COVID-19: An Endemic Model of COVID-19

“…We calculate the control reproduction number using the next generation matrix operator [13,59] on (2.2)-(2.7) as used by [46,51]. The matrix for the rates of new infections F and that of transfer of infected individuals, V at the DFE are given by…”

“…Several mathematical models have been developed and analyzed to study the transmission dynamics of COVID-19 [2,4,26,27,33,53,39,46,66,70]. Bugalia et al [4] developed a COVID-19 model using an endemic framework considering the roles of intervention strategies such as lockdown, hospitalization and quarantine.…”