2.5. Virulence Definition
In this study, we define virulence as the capacity to cause a disease. In order to measure it, we utilize a set of parameters that uniformly increase the rate or probability of causing symptomatic disease or the severity of those symptoms (including death). Our definition is more comprehensive than many other models of parasite virulence (e.g., [4,13]), which tend to focus on a single aspect of the natural history of disease associated with harm to a host (e.g., the fitness consequences of an infection on the host population or the case fatality rate). Instead of having to justify a definition built around a single term (e.g., the term associated with fatality), we took a collective approach to defining virulence through all terms that foment the viral-induced onset of symptomatic disease and death. This definition allows for the reality of pleiotropic effects in viral pathogens, where adaptations can have multiple effects on the natural history of disease [2,33]. Our definition of virulence emphasizes terms that influence host wellness and/or are symptoms of disease. The iteration of virulence used in this study also undermines the potential for overly weighting only one or a small number of parameters under a large umbrella of virulence. Because so many varying definitions exist for virulence, we have also performed calculations according to a different definition of virulence, one that exclusively considers terms that have a detrimental direct effect on the host and neither of the terms that reflect symptoms of severe disease (𝜎a and 𝜎I). These calculations can be found in the Supplementary Materials.
The collection of parameters that we use to define virulence are as follows: the infected population death rate (𝜇I), the incubation period of SARS-CoV-2 (𝜂), the rate of transfer from asymptomatic to symptomatic (1/⍵), the infected population recovery rate (ν), the percent of individuals that move from the asymptomatic to the recovered compartment without showing symptoms (the “mild” recovery track, p), the contact rate of people with people × the transmission probability of people to people by an asymptomatic individual (βA), the contact rate of people with people × the transmission probability of people to people by an asymptomatically infected person (βI), the contact rate of people with the environment × the probability of shedding by an asymptomatic individual to the environmental (𝜎A), the contact rate of people with the environment × the probability of symptomatically infected individuals shedding in the environment (𝜎I), and the average number of days before infection (1/ε).
Table 3 outlines the direction in which each of the virulence-associated parameters are modulated as virulence decreases or increases. An up arrow (↑) indicates the parameter increases (by an equivalent percent) when the percent virulence is changed. A down arrow (↓) indicates the parameter decreases (by an equivalent percent) when the percent change in virulence is applied. Changes in virulence are then defined, in this study, as an equivalent uniform (percent) change in each of the parameters listed above. For the purposes of our study, we modify virulence by changing all parameters associated with virulence by 5%. One could also disambiguate virulence into changes in individual subcomponents; however, that is not the focus of this current study.