COVID-19 outbreak in Mauritius: Logistic growth and SEIR modelling with quarantine and an effective reproduction number

SUMMARY Background and Objectives The island of Mauritius experienced a COVID-19 outbreak from mid-March to end April 2020. The first three cases were reported on March 18 (Day 1) and the last locally transmitted case occurred on April 26 (Day 40). An island confinement was imposed on March 20 followed by a sanitary curfew on March 23. Supermarkets were closed as from March 25 (Day 8). There were a total of 332 cases including 10 deaths from Day 1 to Day 41. Control of the outbreak depended heavily on contact tracing, testing, quarantine measures and the adoption of personal protective measures (PPMs) such as social distancing, the wearing of face masks and personal hygiene by Mauritius inhabitants. Our objectives were to model and understand the evolution of the Mauritius outbreak using mathematical analysis, a logistic growth model and an SEIR compartmental model with quarantine and a reverse sigmoid effective reproduction number and to relate the results to the public health control measures in Mauritius. Methods The daily reported cumulative number of cases in Mauritius were retrieved from the Worldometer website at https://www.worldometers.info/coronavirus/country/mauritius/. A susceptible-exposed-infectious-quarantined-removed (SEIQR) model was introduced and analytically integrated under the assumption that the daily incidence of infectious cases evolved as the derivative of the logistic growth function. The cumulative incidence data was fitted using a logistic growth model. The SEIQR model was integrated computationally with an effective reproduction number (R_e) varying in time according to a three-parameter reverse sigmoid model. Results were compared with the retrieved data and the parameters were optimised using the normalised root mean square error (NRMSE) as a comparative statistic. Findings A closed-form analytical solution was obtained for the time-dependence of the cumulative number of cases. For a small final outbreak size, the solution tends to a logistic growth. The cumulative number of cases was well described by the logistic growth model (NRMSE = 0.0276, R^2=0.9945) and by the SEIQR model (NRMSE = 0.0270, R^2=0.9952) with the optimal parameter values. The value of R_e on the day of the reopening of supermarkets (Day 16) was found to be approximately 1.6. Interpretation A mathematical basis has been obtained for using the logistic growth model to describe the time evolution of outbreaks with a small final outbreak size. The evolution of the outbreak in Mauritius was consistent with one modulated by a time-varying effective reproduction number resulting from the epidemic control measures implemented by Mauritius authorities and the PPMs adopted by Mauritius inhabitants. The value of R_e{approx}1.6 on the reopening of supermarkets on Day 16 was sufficient for the outbreak to grow to large-scale proportions in case the Mauritius population did not comply with the PPMs. However, the number of cases remained contained to a small number which is indicative of a significant contribution of the PPMs in the public health response to the COVID-19 outbreak in Mauritius.