Title

Last modified: 2014-06-09

#### Abstract

Several recent papers have introduced explicit modelling of hosts’ immune response in epidemic dynamics, giving rise to “nested epidemic models” especially in order to discuss the evolution of hosts and pathogens [1,2].If, as assumed in [1], pathogen load at infection is fixed, the model can reduce to an age-of-infection structure, and its qualitative behaviour follows the usual properties of epidemic models, although host heterogeneity in within-host parameters can give rise to relevant evolutionary consequences [3].

On the other hand, if initial infection load depends on the pathogen load of the individual from whom the infection is acquired, the models become much more complex; we present a mathematical framework to handle this case, although some open problems remain.

We have also performed several numerical simulations for the case of a single epidemic wave in a closed population, with different values of the parameters concerning pathogen transmission and isolation of the diseased individuals. Our aims have been, on the one hand, to understand the effects of these parameters on macroscopic features such as R0, final size or mean duration of the epidemics; on the other hand, to compare the model results with those of simpler SIR or SEIR models, matched as for the values of R0, mean length of infectious or latent periods, as could be estimated from the simulations.

A clear difference between models is that the present model yields an epidemic curve to which several smaller waves are in contrast with classical unimodal curve of epidemic models.

Extending the model to endemic infections poses the problem of an effective way to model reinfections, without arriving at an intractable model. Some possible ways of simplifying the problems will be suggested.

REFERENCES

[1]Gilchrist M.A., Sasaki A.,. Modeling host-parasite coevolution. J. theor. Biol. 218: 289--308, 2002. [2]Mideo N., Alizon S., Day T., Linking within- and between-host dynamics in the evolutionary epidemiology of infectious diseases.

*TREE*23:511--517, 2008.

[3] Pugliese A., The role of host population heterogeneity in the evolution of virulence,

*J. Biol. Dynamics*5: 104-119, 2011.