Superinfections can induce evolutionarily stable coexistence of pathogens. (English) Zbl 1141.92028
Summary: Parasites reproduce and are subject to natural selection at several different, but intertwined, levels. M. A. Gilchrist and D. Coombs [Theor. Popul. Biol. 69, No. 2, 145–153 (2006; Zbl 1089.92044)] relate the between-host transmission in the context of an SI model to the dynamics within a host. They demonstrate that within-host selection may lead to an outcome that differs from the outcome of selection at the host population level. We combine the two levels of reproduction by considering the possibility of superinfection and study the evolution of the pathogen’s within-host reproduction rate \(p\). We introduce a superinfection function \(\phi = \phi (p,q)\), giving the probability with which pathogens with trait \(q\), upon transmission to a host that is already infected by pathogens with trait \(p\), “take over” the host.
We consider three cases according to whether the function \(q \rightarrow \phi (p,q)\) (i) has a discontinuity, (ii) is continuous, but not differentiable, or (iii) is differentiable in \(q = p\). We find that in case (i) the within-host selection dominates in the sense that the outcome of evolution at the host population level coincides with the outcome of evolution in a single infected host. In case (iii), it is the transmission to susceptible hosts that dominates the evolution to the extent that the singular strategies are the same as when the possibility of superinfections is ignored. In the biologically most relevant case (ii), both forms of reproduction contribute to the value of a singular trait. We show that when \(\phi \) is derived from a branching process variant of the submodel for the within-host interaction of pathogens and target cells, the superinfection functions fall under case (ii). We furthermore demonstrate that the superinfection model allows for steady coexistence of pathogen traits at the host population level, both on the ecological, as well as on the evolutionary time scale.
We consider three cases according to whether the function \(q \rightarrow \phi (p,q)\) (i) has a discontinuity, (ii) is continuous, but not differentiable, or (iii) is differentiable in \(q = p\). We find that in case (i) the within-host selection dominates in the sense that the outcome of evolution at the host population level coincides with the outcome of evolution in a single infected host. In case (iii), it is the transmission to susceptible hosts that dominates the evolution to the extent that the singular strategies are the same as when the possibility of superinfections is ignored. In the biologically most relevant case (ii), both forms of reproduction contribute to the value of a singular trait. We show that when \(\phi \) is derived from a branching process variant of the submodel for the within-host interaction of pathogens and target cells, the superinfection functions fall under case (ii). We furthermore demonstrate that the superinfection model allows for steady coexistence of pathogen traits at the host population level, both on the ecological, as well as on the evolutionary time scale.
MSC:
| 92D15 | Problems related to evolution |
| 92D30 | Epidemiology |
| 37N25 | Dynamical systems in biology |
| 91A99 | Game theory |
| 92D25 | Population dynamics (general) |
Keywords:
virulence; evolutionary branching; ESS; CSS; basic reproduction ratio; superinfection; invasibility; optimization; within-host dynamics; pathogen; nested model; pairwise invasibility plot; coexistence; evolutionary suicide; singular strategy; dimorphism; virusCitations:
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