Evolution of COVID-19 cases in selected low- and middle-income countries: past the herd immunity peak? (preprint)

ABSTRACT

We have studied the evolution of COVID-19 in 12 low and middle income countries in which reported cases have peaked and declined rapidly in the past 2-3 months. In most of these countries the declines happened while control measures were consistent or even relaxing, and without signs of significant increases in cases that might indicate second waves. For the 12 countries we studied, the hypothesis that these countries have reached herd immunity warrants serious consideration. The Reed-Frost model, perhaps the simplest description for the evolution of cases in an epidemic, with only a few constant parameters, fits the observed case data remarkably well, and yields parameter values that are reasonable. The best-fitting curves suggest that the effective basic reproduction number in these countries ranged between 1.5 and 2.0, indicating that the curve was flattened in some countries but not suppressed by pushing the reproduction number below 1. The results suggest that between 51 and 80% of the population in these countries have been infected, and that between 0.05% and 2.50% of cases have been detected; values which are consistent with findings from serological and T-cell immunity studies. The infection rates, combined with data and estimates for deaths from COVID-19, allow us to estimate overall infection fatality rates for three of the countries. The values are lower than expected from reported infection fatality rates by age, based on data from several high-income countries, and the country population by age. COVID-19 may have a lower mortality risk in these three countries (to differing degrees in each country) than in high-income countries, due to differences in immune response, prior exposure to coronaviruses, disease characteristics or other factors. We find that the herd immunity hypothesis would not have fit the evolution of reported cases in several European countries, even just after the initial peaks; and subsequent resurgences of cases obviously prove that those countries have infection rates well below herd immunity levels. Our hypothesis that the 12 countries we studied have reached herd immunity should now be tested further, through serological and T cell immunity studies.