Mathematical Model of SARS-Cov-2 Propagation Versus ACE2 Fits COVID-19 Lethality Across Age and Sex and Predicts That of SARS

Abstract

The fatality rate of Covid-19 escalates with age and is larger in men than women. I show that these variations correlate strongly with the level of the viral receptor protein ACE2 in rat lungs, which is consistent with the still limited data on human ACE2. Surprisingly, lower receptor levels correlate with higher fatality. I propose two possible explanations of this negative correlation: First, a previous mathematical model predicts that the velocity of viral progression in the organism as a function of the receptor level has a maximum and declines for abundant receptor. Secondly, degradation of ACE2 by the virus may cause the runaway inflammatory response that characterizes severe CoViD-19. I present here a mathematical model that predicts the lethality as a function of ACE2 protein level based on the two above hypothesis. The model fits Covid-19 fatality rate across age and sex in three countries with high accuracy ( $r^2>0.9$ ) under the hypothesis that the speed of viral progression in the infected organism is a decreasing function of the ACE2 level. Moreover, rescaling the fitted parameters by the ratio of the binding rates of the spike proteins of SARS-CoV and SARS-CoV-2 allows predicting the fatality rate of SARS-CoV across age and sex, thus linking the molecular and epidemiological levels.

Keywords: ACE2; COVID-19; SARS-CoV-2; inflammatory response; mathematical model; viral propagation.