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We present an SI epidemic model whereby a continuous variable capturesvariability in proliferative potential and resistance to infection amongsusceptibles. The occurrence of heritable, spontaneous changes in thesephenotype and the presence of a fitness trade-off between resistance toinfection and proliferative potential are incorporated into the model. Themodel comprises an ODE for the number of infected individuals that is coupledwith a partial integrodifferential equation for the population density ofsusceptibles through an integral term. The expression for the basicreproduction number $\mathcal{R}_0$ is derived, the disease-free and endemicequilibrium of the model are characterised and a threshold theorem is proved.Analytical results are integrated with numerical simulations of a calibratedversion of the model based on the results of artificial selection experimentsin a host-parasite system. The results of our mathematical study disentanglethe impact of different evolutionary parameters on the spread of infectiousdiseases and the consequent phenotypic adaption of susceptible individuals. Inparticular, these results provide a theoretical basis for the observation thatinfectious diseases exerting stronger selective pressures on susceptibles andbeing characterised by higher infection rates are more likely to spread.Moreover, our results indicate that spontaneous phenotypic changes inproliferative potential and resistance to infection can either promote orprevent the spread of diseases depending on the strength of selection acting onsusceptible individuals prior to infection. Finally, we demonstrate that, whenan endemic equilibrium is established, higher levels of resistance to infectionand lower degrees of phenotypic heterogeneity are to be expected in thepresence of infections which are characterised by lower rates of death andexert stronger selective pressures.

Evolutionary dynamics in an SI epidemic model with phenotype-structured susceptible compartment