Dynamics in a simple evolutionary-epidemiological model for the evolution of an initial asymptomatic infection stage

• Published in: Proceedings of the National Academy of Sciences - PNAS 2020-05, Vol.117 (21), p.11541-11550
• Main Authors: Saad-Roy, Chadi M., Wingreen, Ned S., Levin, Simon A., Grenfell, Bryan T.
• Format: Article
• Language: English
• Subjects: Asymptomatic infection; Asymptomatic Infections - epidemiology; Biological Evolution; Biological Sciences; Bistability; Disease control; Disease Progression; Disease Transmission, Infectious; Epidemic models; Epidemiology; Evolution; Evolutionarily stable strategy; Host-Pathogen Interactions; Humans; Immunology; Infections; Latency; Life history; Mathematical models; Models, Biological; Natural selection; Pathogens; Strategy; Tradeoffs; Virus Diseases - epidemiology; Virus Diseases - transmission; Virus Diseases - virology
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.1920761117

Pathogens exhibit a rich variety of life history strategies, shaped by natural selection. An important pathogen life history characteristic is the propensity to induce an asymptomatic yet productive (transmissive) stage at the beginning of an infection. This characteristic is subject to complex trade-offs, ranging from immunological considerations to population-level social processes. We aim to classify the evolutionary dynamics of such asymptomatic behavior of pathogens (hereafter “latency”) in order to unify epidemiology and evolution for this life history strategy. We focus on a simple epidemiological model with two infectious stages, where hosts in the first stage can be partially or fully asymptomatic. Immunologically, there is a trade-off between transmission and progression in this first stage. For arbitrary trade-offs, we derive different conditions that guarantee either at least one evolutionarily stable strategy (ESS) at zero, some, or maximal latency of the first stage or, perhaps surprisingly, at least one unstable evolutionarily singular strategy. In this latter case, there is bistability between zero and nonzero (possibly maximal) latency. We then prove the uniqueness of interior evolutionarily singular strategies for power-law and exponential trade-offs: Thus, bistability is always between zero and maximal latency. Overall, previous multistage infection models can be summarized with a single model that includes evolutionary processes acting on latency. Since small changes in parameter values can lead to abrupt transitions in evolutionary dynamics, appropriate disease control strategies could have a substantial impact on the evolution of first-stage latency.