title: Epidemic cycling in a multi-strain SIRS epidemic network model.
abstract: BACKGROUND
  One common observation in infectious diseases caused by multi-strain pathogens is that both the incidence of all infections and the relative fraction of infection with each strain oscillate with time (i.e., so-called Epidemic cycling). Many different mechanisms have been proposed for the pervasive nature of epidemic cycling. Nevertheless, the two facts that people contact each other through a network rather than following a simple mass-action law and most infectious diseases involve multiple strains have not been considered together for their influence on the epidemic cycling.
  
  
  METHODS
  To demonstrate how the structural contacts among people influences the dynamical patterns of multi-strain pathogens, we investigate a two strain epidemic model in a network where every individual randomly contacts with a fixed number of other individuals. The standard pair approximation is applied to describe the changing numbers of individuals in different infection states and contact pairs.
  
  
  RESULTS
  We show that spatial correlation due to contact network and interactions between strains through both ecological interference and immune response interact to generate epidemic cycling. Compared to one strain epidemic model, the two strain model presented here can generate epidemic cycling within a much wider parameter range that covers many infectious diseases.
  
  
  CONCLUSIONS
  Our results suggest that co-circulation of multiple strains within a contact network provides an explanation for epidemic cycling.
authors.affiliation: Department of Statistics, Modelling and Economics, Centre for Infectious Disease Surveillance and Control, Public Health England, 61 Colindale Avenue, London, NW9 5EQ, UK. xu-sheng.zhang@phe.gov.uk.|Medical Research Council Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College School of Public Health, Norfolk Place, London, W2 1PG, UK. xu-sheng.zhang@phe.gov.uk.
authors.forename: Xu-Sheng
authors.initials: XS
authors.lastname: Zhang
mesh_terms: D002648:Child; D003140:Communicable Disease Control; D003141:Communicable Diseases / Q000453:epidemiology; D004196:Disease Outbreaks; D004463:Ecology; D058872:Epidemics; D006801:Humans; D007107:Immune System; D015994:Incidence; D055552:Infectious Disease Medicine / Q000379:methods; D015233:Models, Statistical; D009991:Oscillometry; D010641:Phenotype; D013269:Stochastic Processes; D018746:Systemic Inflammatory Response Syndrome / Q000453:epidemiology*
keywords: Competition; Contact network; Cross-immunity; Cyclical dominance of strains; Infectious diseases; Oscillatory epidemics