Mathematical modeling of COVID-19 containment strategies with considerations for limited medical resources

Brydon Eastman; Cameron Meaney; Michelle Przedborski; Mohammad Kohandel

The interpretations of the individual terms in the SEIRD model are given in Eq. (A.1). As illustrated by the set of ordinary differential equations (ODEs) in Eq. (A.1), the SEIRD model depends upon four kinetic parameters. The parameter β controls the rate of virus transmission from infected to susceptible individuals. It is determined by the probability of disease transmission as well as the chance of contact, thus it indirectly incorporates the basic reproduction number, R 0 , of the virus and the proportion of individuals who are social distancing. The mean latent period, which is the average length of time between exposure to the virus and the point at which an individual becomes contagious, is given by γ −1 . The rate at which infectious individuals are removed from the disease (either via recovery or death) is given by (α + δ), thus the value of (α + δ) −1 is the mean length of time an infected individual is contagious before they either recover or die from the disease. The five compartments are subjected to the constraint S + E + I + R + D = N , where N is the total population. We point out that the state equations are considered to represent direct counts of the population size in this work, rather than proportions of the population. Note that, due to the form of the equations, the parameter β in Model 1 includes division by the total population size N .