Epidemiological and evolutionary consequences of periodicity in treatment coverage

Abstract

Host heterogeneity is a key driver of host–pathogen dynamics. In particular, the use of treatments against infectious diseases creates variation in quality among hosts, which can have both epidemiological and evolutionary consequences. We present a general theoretical model to highlight the consequences of different imperfect treatments on pathogen prevalence and evolution. These treatments differ in their action on host and pathogen traits. In contrast with previous studies, we assume that treatment coverage can vary in time, as in seasonal or pulsed treatment strategies. We show that periodic treatment strategies can limit both disease spread and virulence evolution, depending on the type of treatment. We also introduce a new method to analytically calculate the selection gradient in periodic environments, which allows our predictions to be interpreted using the concept of reproductive value, and can be applied more generally to analyse eco-evolutionary dynamics in class-structured populations and fluctuating environments.

Evolution of class-structured populations in periodic environments

“…This useful result allows us to rewrite the average selection gradient as where we have neglected the covariances Cov( c k , ω k ) that arise when taking the mean. Extensive numerical simulations show that this approximation fits very well the prediction of a Floquet analysis (Walter & Lion, 2021).…”

“…Hence the mean value of the class reproductive value converges towards 1/2, and the selection gradient simplies to . With a trade-off α A = z , α B = (1 − r a ) z and β B = β A = β 0 z/ (1 + z ), the ES virulence for large periods has the very simple expression: (see also Walter & Lion (2021) for a slightly more general result). Finally, we note that the dynamics of the individual reproductive values can be used to show that, for a vaccine that linearly reduces transmission (i.e. r a = 0 and r b > 0), we have which means that, although the reproductive values fluctuate due to the dynamics of the host densities, their ratio v A ( t ) /v B ( t ) remains constant and equal to 1/(1 − r b ) at all times.…”

“…Hence the mean value of the class reproductive value converges towards 1/2, and the selection gradient simplies to . With a trade-off α A = z , α B = (1 − r a ) z and β B = β A = β 0 z/ (1 + z ), the ES virulence for large periods has the very simple expression: (see also Walter & Lion (2021) for a slightly more general result).…”

“…An interesting consequence is that, when the period of fluctuations increases, 〈 c A 〉 increases (figure 6d), which selects for lower virulence compared to a scenario with constant vaccination coverage (figure 6c). For large periods, 〈 c A 〉 converges towards 1/2 (the mean of ν ( t )), which allows the ES virulence to be analytically calculated (Walter & Lion (2021), appendix S.3). Note that, in the latter figure, the slight quantitative discrepancy between the prediction of equation (29) and the Floquet analysis is due to the fact that we have neglected the covariances Cov ( c k , ω k ).…”

Evolutionary epidemiology consequences of trait-dependent control of heterogeneous parasites

“…Different transmission functions may also emerge as a consequence of physiological alterations of hosts’ level of activity, in the case of animal (and human) systems, and of intervention policies in the context of human disease modelling (quarantine, contact tracing, etc…). Our framework might also be relevant to study the optimisation of inevitably imperfect treatments 44 , such as a potential eradication-protection trade-off: indeed, due to its inhibitory action on transmission events, an investment in the protectant contribution is expected to be efficient whenever the infected population is in a high-transmission state. However, if such investment is paid for by a reduced eradicant effect, it is not obvious how the pathogen would adapt to such intervention; hence, the importance of a tool able to predict the trait distribution.…”