[Paper Review] An epidemiological model for the spread of COVID-19: A South African case study

Olivier Le, Craig Ik|arXiv (Cornell University)|May 16, 2020

COVID-19 epidemiological studies7 references4 citations

TL;DR

This study develops an SEIQRDP epidemiological model to forecast the spread of COVID-19 in South Africa, using parameterization from Germany, Italy, and South Korea to calibrate transmission dynamics. When constrained by reported basic reproduction numbers, the model predicts a peak in infectious cases by late October 2020 and total deaths ranging from 10,000 to 90,000, with a nominal estimate of 22,000, highlighting strong sensitivity to control measures and R₀ values.

ABSTRACT

An epidemiological model is developed for the spread of COVID-19 in South Africa. A variant of the classical compartmental SEIR model, called the SEIQRDP model, is used. As South Africa is still in the early phases of the global COVID-19 pandemic with the confirmed infectious cases not having peaked, the SEIQRDP model is first parameterized on data for Germany, Italy, and South Korea - countries for which the number of infectious cases are well past their peaks. Good fits are achieved with reasonable predictions of where the number of COVID-19 confirmed cases, deaths, and recovered cases will end up and by when. South African data for the period from 23 March to 8 May 2020 is then used to obtain SEIQRDP model parameters. It is found that the model fits the initial disease progression well, but that the long-term predictive capability of the model is rather poor. The South African SEIQRDP model is subsequently recalculated with the basic reproduction number constrained to reported values. The resulting model fits the data well, and long-term predictions appear to be reasonable. The South African SEIQRDP model predicts that the peak in the number of confirmed infectious individuals will occur at the end of October 2020, and that the total number of deaths will range from about 10,000 to 90,000, with a nominal value of about 22,000. All of these predictions are heavily dependent on the disease control measures in place, and the adherence to these measures. These predictions are further shown to be particularly sensitive to parameters used to determine the basic reproduction number. The future aim is to use a feedback control approach together with the South African SEIQRDP model to determine the epidemiological impact of varying lockdown levels proposed by the South African Government.

Motivation & Objective

• To develop a compartmental epidemiological model tailored to South Africa’s early-stage COVID-19 pandemic dynamics.
• To calibrate model parameters using data from countries with well-documented epidemic peaks—Germany, Italy, and South Korea.
• To assess the predictive accuracy of the SEIQRDP model when applied to South African data from March 23 to May 8, 2020.
• To improve long-term forecast reliability by constraining the basic reproduction number to empirically reported values.
• To explore the potential of using feedback control with the model to evaluate varying lockdown strategies in South Africa.

Proposed method

• An extended SEIQRDP compartmental model is employed, incorporating susceptible, exposed, infectious, quarantined, recovered, deceased, and protected compartments.
• Model parameters are initially estimated using confirmed case, death, and recovery data from Germany, Italy, and South Korea, where epidemic curves had passed their peaks.
• South African data from March 23 to May 8, 2020, is used to recalibrate the model and assess initial fit and predictive performance.
• The basic reproduction number (R₀) is constrained to reported values to improve model stability and long-term forecast reliability.
• Sensitivity analysis is performed to evaluate the impact of R₀ and control measures on predicted outcomes.
• A feedback control framework is proposed for future use to simulate and evaluate the epidemiological impact of different lockdown levels.

Experimental results

Research questions

• RQ1 How well can the SEIQRDP model predict the trajectory of COVID-19 in South Africa using early epidemic data?
• RQ2 What is the impact of constraining the basic reproduction number on model accuracy and long-term forecast reliability?
• RQ3 When is the predicted peak of infectious cases expected in South Africa under current control measures?
• RQ4 What range of total deaths is projected by the model, and how sensitive are these projections to R₀ and intervention adherence?
• RQ5 How can feedback control mechanisms be integrated with the SEIQRDP model to evaluate alternative lockdown strategies?

Key findings

• The SEIQRDP model fits the initial phase of South Africa’s epidemic well when calibrated with international data, but long-term predictions are unreliable without constraints.
• Constraining the basic reproduction number to reported values significantly improves model fit and enhances long-term predictive capability.
• The model predicts a peak in confirmed infectious individuals around late October 2020.
• Total cumulative deaths are projected to range from 10,000 to 90,000, with a nominal estimate of approximately 22,000.
• Predictions are highly sensitive to the value of the basic reproduction number and to the level of adherence to public health control measures.
• The study identifies a clear need for integrating feedback control mechanisms with the model to evaluate and optimize future lockdown policies.