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

Brydon Eastman; Cameron Meaney; Michelle Przedborski; Mohammad Kohandel

In the proposed model, the parameters β DD , β DM , β M D , and β M M have been introduced to represent the rate of virus transmission from infected to susceptible individuals, while taking into account the social distancing practices. Specifically, β DD , controls the rate of transmission from infected distancers to susceptible distancers, β DM from infected distancers to susceptible mixers, β M D from infected mixers to susceptible distancers, and β M M from infected mixers to susceptible mixers. Intuitively, individuals who practice social distancing are less likely to come into contact with others and transmit the virus. Thus we assume that β DD < β DM = β M D < β M M . These assumptions imply that individuals who practice social distancing are least likely to pass the disease to one another and that individuals who do not practice social distancing are most likely to pass the disease to one another. Furthermore, by assigning β DM = β M D , we are making the simplifying assumption that a susceptible distancer is equally likely to come into contact with an infectious mixer as a susceptible mixer is to come into contact with an infectious distancer. Moreover, we assume that this cross-compartment transmission rate falls between the two inter-compartment transmission rates. Similarly, while the pairs of parameters γ M and γ D , α M and α D , and δ M and δ D are theoretically different, we assume that each pair is the same across compartments. That is, we assume that γ M = γ D , α M = α D , and δ M = δ D and drop the subscripts. Effectively, we are assuming that the behaviour of social distancing has minimal effect on the values of these parameters. That is to say, we assume that the latent period γ −1 and the mean infectious length (α + δ) −1 are functions entirely of the disease and are not influenced by behaviour.