Browsing by Subject "superinfection"
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(2017)Recent biomathematical literature has suggested that, under the assumption of a trade-off between replication speed and fidelity, a pathogen can evolve to more than one optimal mutation rate. O'Fallon (2011) presents a particularly compelling case grounded in simulation. In this thesis, we treat the subject analytically, approaching it through the lens of adaptive dynamics. We formulate a within-host model of the pathogen load starting from assumptions at the genomic level, explicitly accounting for the fact that most mutations are deleterious and stunt growth. We single out the pathogen's mutation probability as the evolving trait that distinguishes strains from one another. Our between-host dynamics take the form of an SI model, first without superinfection and later with two types of non-smooth superinfection function. The pathogen's virulence and transmission rate are functions of the within-host equilibrium pathogen densities. In the case of our mechanistically defined superinfection function, we uncover evolutionary branching in conjunction with two transmission functions, one a caricatural (expansion) example, the other a more biologically realistic (logistic) one. Because of the non-smoothness of the mechanistic superinfection function, our branching points are actually one-sided ESSs à la Boldin and Diekmann (2014). When branching occurs, two strains with different mutation probabilities both ultimately persist on the evolutionary timescale.
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(2023)In this thesis, we study epidemic models such as SIR and superinfection to demonstrate the coexistence as well as the competitive exclusion of all but one strain. We show that the strain that can keep its position under the worst environmental conditions cannot be invaded by any other strain when it comes to some models with a constant death rate. Otherwise, the optimization principle does not necessarily work. Nevertheless, Ackleh and Allen proved that in the SIR model with a density-dependent mortality rate and total cross-immunity the strain with the largest basic reproduction number is the winner in competitive exclusion. However, it must be taken into account that the conditions on the parameters used for the proof are sufficient but not necessary to exclude the coexistence of different pathogen strains. We show that the method can be applied to both density-dependent and frequency-dependent transmission incidence. In the latter half, we link the between and within-host models and expand the nested model to allow for superinfection. The introduction of the basic notions of adaptive dynamics contributes to simplifying our task of demonstrating the evolutionary branching leading to diverging dimorphism. The precise conclusions about the outcome of evolution will depend on the host demography as well as on the class of superinfection and the shape of transmission functions.
Now showing items 1-2 of 2