Abstract
Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance between strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the “one disease equals one pathogen” paradigm.
Highlights
Viral species are known to often undergo rapid evolution
Most pathogens circulate under a family of strains which can interact differently with the host immune system and undergo further mutations
We introduce a multistrain Susceptible-Infectious-Recovered-Susceptible epidemic model with an underlying genotype network, allowing the disease to evolve along plausible mutation pathways as it spreads in a well-mixed population
Summary
Viral species are known to often undergo rapid evolution. Since the early 20th century, influenza viruses have been described as having marked variability and unpredictable behaviour [1]. Subsequent RNA virus studies of the 20th and 21st century have focused on, among others, the Zaire ebolavirus, strains of the SARS-CoV species, and HIV-1, all possessing high mutation rates [2]. These frequent mutations contribute to the antigenic evolution of these viruses, allowing them to evade recognition by the human immune system [3]. Despite the long-standing knowledge of subtypes and strains within viral species, mathematical disease modelling has continued to model viral diseases with one underlying pathogen. Models which fail to account for antigenic variation of a pathogen may lead to biased characterizations of epidemic emergence and progression
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