Pathogen fitness as a function of virulence (Frank, 1996)
1 Pathogen fitness as function of virulence
(Frank 1996) provides an alternate formulation of virulence-transmission trade-off which defines pathogen fitness as a product of increase in capacity for transmission success for a particular pathogen reproductive intensity, weighted or scaled by the reduction in opportunity, duration, or effectiveness in transmission due to damage to the host due to the virulence of that reproductive intensity.
The fitness of a pathogen can be measured by the net gain in infected hosts, \(w\),
\[ w = z f(z), \tag{1}\]
where:
- \(w\) is the pathogen fitness (corresponding to \(R_0\), the net total reproductive output of the virus in terms of newly infected hosts),
- \(z\) is a measure correlated positively with parasite reproductive intensity, which correlates positively with capacity for transmission success, as measured by the number of hosts infected by a single infected host given full transmission opportunity (if host fitness, longevity, resources, mobility, etc. were not impacted by virus reproductive activity),
- \(f(z)\), a “declining function of \(z\)” (meaning that \(f(z)\) decreases as \(z\) increases), which is the cost or penalty factor accounting for reduction in transmission success due to depletion of host resources, fitness, longevity and so on as a result of pa.
2 Linear decline in host resources due to virulence
(Frank 1996) describes a linear function to model the degradation of the host resources available due to virulence, \(f(z) = 1 - \alpha z\), where \(\alpha\) is a scaling relation between transmission (\(z\)) and virulence (\(\alpha z\)).
The pathogen fitness function under this linear scaling is
\[ \begin{align} w = z (1 - \alpha z) \end{align} \tag{2}\]