On the Dynamic Interaction of Social Processes and COVID-19 Infection Dynamics (preprint)

Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave, had subsequent waves of the COVID-19 infections and it remains to be seen whether there will be more waves. In this paper, we formulate a deterministic model for COVID-19 incorporating dynamic non-pharmaceutical interventions, dubbed social dynamics. The model steady states are determined and their stability analysed. Numerical simulations are carried out to determine the pack of various parameters that influence the social dynamics. In South Africa, the first wave was the only wave in which the only interventions rested solely on human behavior. The model is thus fitted to COVID-19 data on the first wave in South Africa. The results presented in this paper have implications on the trajectory of the pandemic in the presence of changing social processes.

Mathematical modelling of COVID-19 with periodic transmission: The case of South Africa (preprint)

The data on SARS-CoV-2 (COVID-19) in South Africa shows seasonal transmission patterns to date, with the peaks having occurred in winter and summer since the outbreaks began. The transmission dynamics have mainly been driven by variations in environmental factors and virus evolution, and the two are at the center of driving the different waves of the disease. It is thus important to understand the role of seasonality in the transmission dynamics of COVID-19. In this paper, a compartmental model with a time-dependent transmission rate is formulated and the stabilities of the steady states analysed. We note that if R0 < 1, the disease-free equilibrium is globally asymptotically stable, and the disease completely dies out and when R0 > 1, the system admits a positive periodic solution, and the disease is uniformly or periodically persistent. The model is fitted to data on new cases in South Africa for the first four waves. The model results clearly indicate the need to consider seasonality in the transmission dynamics of COVID-19 and its importance in modelling fluctuations in the data for new cases. The potential impact of seasonality in the transmission patterns of COVID-19 and the public health implications are discussed.

Modelling the potential role of super spreaders on COVID-19 transmission dynamics (preprint)

Superspreading phenomenon has been observed in many infectious diseases and contributes significantly to public health burden in many countries. Superspreading events have recently been reported in the transmission of the COVID-19 pandemic. The present study uses a set of nine ordinary differential equations to investigate the impact of superspreading on COVID-19 dynamics. The model developed in this study addresses the heterogeineity in infectiousness by taking into account two forms of transmission rate functions for superspreaders based on clinical (infectivity level) and social or environmental (contact level). The basic reproduction number has been derived and the contribution of each infectious compartment towards the generation of new COVID-19 cases is ascertained. Data fitting was performed and parameter values were estimated within plausible ranges. Numerical simulations performed suggest that control measures that decrease the effective contact radius and increase the transmission rate exponent will be greatly beneficial in the control of COVID-19 in the presence of superspreading phenomena.

A COVID-19 model with a nonlinear incidence rate and intervention exit strategies for Kenya (preprint)

The coronavirus disease (COVID-19) is a novel infection caused by SARS-CoV-2, a corona virus type that has previously not been seen in humans. The speedy spread of COVID-19 globally has greatly affected the socio-economic environments and health systems. To effectively address this rapid spread, it is imperative to have a clear understanding of the COVID-19 transmission dynamics. In this study we evaluate a COVID-19 epidemic model with a nonlinear incidence function and a saturating. We propose an SLIHRD data driven COVID 19 model which incorporates individual self initiated behavior change of the susceptible individuals. The proposed model allows the evaluation of the impact of easing intervention measures at specific times. To estimate the model parameters, the model was fitted to the daily reported COVID-19 cases in Kenya. Self initiated behavioral responses by individuals and large scale persistent testing proved to be the most effective measures to flatten the epidemic infection curve.The model illustrates the effect of mass testing on COVID-19 as well as individual self initiated behavioral change when the number of infected individuals increases. The results have significant impact on the management of COVID-19 and implementation of prevention policies.

Application of Optimal Control to Long Term Dynamics of COVID-19 Disease in South Africa (preprint)

SARS-CoV-2 (COVID-19) belongs to the beta-coronavirus family, these include; the severe acute respiratory syndrome coronavirus (SARS-CoV) and the Middle East respiratory syndrome coronavirus (MERS-CoV). Since its resurgence in South Africa in March 2020, it has lead to high mortality and thousands of people contracting the virus. In this study, we use a set of five differential equations to analyse the effects on long term dynamics of COVID-19 pandemic with optimal control measures. Mathematical analyses of the model without control were done and the basic reproduction number (R0) of the COVID-19 for the South African epidemic determined. The model steady states were also determined, and their analyses presented based on R0: We introduced permissible control measures and formulated an optimal control problem using the Pontraygain Maximum Principle. Our numerical findings suggest that joint implementation of effective mask usage, physical distancing and active screening and testing are effective measures to curtail the spread of the disease on undiagnosed humans. The results obtained in this paper are of public health importance in the control and management of the spread for the novel coronavirus, SARS-CoV-2, in South Africa.

Quantifying early COVID-19 outbreak transmission in South Africa and exploring vaccine efficacy scenarios (preprint)

Background: COVID-19 has emerged and spread at great speed globally and has presented one of the greatest public health challenges in modern times with no proven cure or vac-cine. Africa is still early in this epidemic, therefore the spectrum of disease severity is not yet clear. Methods: We used a mathematical model to fit to the observed cases of COVID-19 in South Africa to estimate the basic reproductive number and critical vaccination coverages to con-trol the disease for different hypothetical vaccine efficacy scenarios. We also estimated the percentage reduction in effective contacts due to the social distancing measures imple-mented. Results: Early model estimates show that COVID-19 outbreak in South Africa had a basic reproductive number of 2.95 (95% credible interval [CrI] 2.83-3.33). A vaccine with 70% effi-cacy had the capacity to contain COVID-19 outbreak but at very higher vaccination cover-age 94.44% (95% Crl 92.44-99.92%) with a vaccine of 100% efficacy requiring 66.10% (95% Crl 64.72-69.95%) coverage. Social distancing measures put in place have so far reduced the number of social contacts by 80.31% (95% Crl 79.76-80.85%). Conclusions: Findings suggest a highly efficacious vaccine would have been required to con-tain COVID-19 in South Africa. Therefore, the current social distancing measures to reduce contacts will remain key in controlling the infection in the absence of vaccines and other therapeutics.

Modelling the potential impact of social distancing on the COVID-19 epidemic in South Africa (preprint)

The novel coronavirus (COVID-19) pandemic continues to be a global health problem whose impact has been significantly felt in South Africa. Social distancing has been touted as the best form of response in managing a rapid increase in the number of infected cases. In this paper, we present a deterministic model to model the impact of social distancing on the transmission dynamics of COVID-19 in South Africa. The model is fitted to the currently available data on the cumulative number of infected cases and a scenario analysis on different levels of social distancing are presented. The results show a continued rise in the number of cases in the lock down period with the current levels of social distancing albeit at a lower rate. The model shows that the number of cases will rise to above 4000 cases by the end of the lockdown. The model also looks at the impact of relaxing the social distancing measures after the initial announcement of the lock down measures. A relaxation of the social distancing by 2% can result in a 23% rise in the number of cumulative cases while on the other hand increasing the levels of social distancing by 2% would reduce the number of cumulative cases by about 18%. These results have implications on the management and policy direction in the early phases of the epidemic.