Fig. 1. Flow diagram of the epidemiological components of the model described in Results.

We have modified the basic SEIR formulation by dividing the exposed (E) and infectious (I) classes into two sequential classes, E₁ and E₂ and I₁ and I₂. Exposed hosts, who are not yet infectious are classified as E₁, while asymptomatic, contagious hosts are classified as E₂. We assume that E₁ individuals transform to E₂ at an exponential rate determined by ϕ₁. The presymptomatic hosts, E₂, transform to symptomatic infected hosts, I₁, at a rate ϕ₂. Both E₂ and I₁ are infectious. This rate largely determines the duration of time during which exposed hosts are able to transmit infection before they show symptoms of infection. If ϕ₂ is large (∼365; around 1 day), then exposed hosts quickly exhibit signs of symptoms and can be identified as infectious (as occurred with SARS). In contrast, if ϕ₂ is slower (∼365/7; a week), then asymptomatic hosts may transmit the disease for up to a week before showing symptoms, as in the case of COVID-19 (or many years in the case of HIV or tuberculosis, when ϕ₂ may range from 0.1 to 0.5). In a similar way, infected hosts, I₁, may become sick and get hospitalized, I₂. These hosts have a higher mortality rate but are assumed to be in relative isolation and are thus unable to transmit the pathogen, except to unprotected health care workers. The majority of the pathogen-induced mortality occurs in the I₂ class. We also include an additional class, C, into our model structure; these are contacts of infectious hosts who do not develop infection. Contact tracing identifies C + E₁ + E₂ as contacts of infected hosts; testing is used to differentiate uninfected contacts, C, from exposed hosts (E₁ and E₂); the former can return to work, and the latter remain in isolation and go on to develop infection.