If we cannot eliminate them, should we tame them? Mathematics underpinning the dose effect of virus infection and its application on covid-19 virulence evolution
Authors: Xu Zhaobin , Zhang Hongmei 
Published: July 2021

AbstractThere is a dose effect in the infection process, that is, different initial virus invasion loads will lead to nonlinear changes in infection probability. Experiments already proved that there was a sigmoid functional relationship between virus infection probability and inoculum dose. By means of mathematical simulation of stochastic process, we theoretically demonstrate that there is a sigmoid function relationship between them. At the same time, our model found three factors that influence the severity of infection symptoms, those are virus toxicity, virus invasion dose and host immunity respectively. Therefore, the mortality rate cannot directly reflect the change of virus toxicity, but is the result of the comprehensive action of these three factors. Protective measures such as masks can effectively reduce the severity of infection while reducing the probability of infection. Based on the sigmoid function relationship between virus infection probability and initial virus invasion dose, we deduce that for highly infectious viruses, such as SARS-COV-2, the evolution of its toxicity is closely related to the host population density, and its toxicity will first increase and then decrease with the increase of host population density. That is to say, on the basis of extremely low host population density, increasing population density is beneficial to the development of virus towards strong toxicity. However, this trend is not sustainable, and there is a turning point of population density. Beyond this turning point, increasing population density will be beneficial to the development of virus towards weak toxicity. This theory can well explain the differences of mortality in Covid-19 in different countries. Countries with high population density and extremely low population density often correspond to lower mortality, while countries with population density in the range of 20-100/km2often have higher mortality. At the same time, we propose that social distance and masks can effectively accelerate the evolution of virus towards low toxicity, so we should not give up simple and effective protection measures while emphasizing vaccination.HighlightsThrough mathematical simulation of random process, we prove the sigmoid function relationship between virus infection probability and initial virus invasion dose theoretically.Our model found three factors that influence the severity of infection symptoms: virus toxicity, virus invasion dose and host immunity. This can help explain why the average infection age was declining as the epidemic went through.With the increase of host population density, virus toxicity will increase at first and then decrease, which will explain the difference of mortality in different population density areas.From the mathematical level, social distance, masks and other protective measures were proved to be positive in promoting the virus evolving into the less toxicity one. Vaccination could also promote virus virulence attenuation.