title: Strain Interactions as a Mechanism for Dominant Strain Alternation and Incidence Oscillation in Infectious Diseases: Seasonal Influenza as a Case Study.
abstract: BACKGROUND
  Many human infectious diseases are caused by pathogens that have multiple strains and show oscillation in infection incidence and alternation of dominant strains which together are referred to as epidemic cycling. Understanding the underlying mechanisms of epidemic cycling is essential for forecasting outbreaks of epidemics and therefore important for public health planning. Current theoretical effort is mainly focused on the factors that are extrinsic to the pathogens themselves ("extrinsic factors") such as environmental variation and seasonal change in human behaviours and susceptibility. Nevertheless, co-circulation of different strains of a pathogen was usually observed and thus strains interact with one another within concurrent infection and during sequential infection. The existence of these intrinsic factors is common and may be involved in the generation of epidemic cycling of multi-strain pathogens.
  
  
  RESULTS
  To explore the mechanisms that are intrinsic to the pathogens themselves ("intrinsic factors") for epidemic cycling, we consider a multi-strain SIRS model including cross-immunity and infectivity enhancement and use seasonal influenza as an example to parameterize the model. The Kullback-Leibler information distance was calculated to measure the match between the model outputs and the typical features of seasonal flu (an outbreak duration of 11 weeks and an annual attack rate of 15%). Results show that interactions among strains can generate seasonal influenza with these characteristic features, provided that: the infectivity of a single strain within concurrent infection is enhanced 2-7 times that within a single infection; cross-immunity as a result of past infection is 0.5-0.8 and lasts 2-9 years; while other parameters are within their widely accepted ranges (such as a 2-3 day infectious period and the basic reproductive number of 1.8-3.0). Moreover, the observed alternation of the dominant strain among epidemics emerges naturally from the best fit model. Alternative modelling that also includes seasonal forcing in transmissibility shows that both external mechanisms (i.e. seasonal forcing) and the intrinsic mechanisms (i.e., strain interactions) are equally able to generate the observed time-series in seasonal flu.
  
  
  CONCLUSIONS
  The intrinsic mechanism of strain interactions alone can generate the observed patterns of seasonal flu epidemics, but according to Kullback-Leibler information distance the importance of extrinsic mechanisms cannot be excluded. The intrinsic mechanism illustrated here to explain seasonal flu may also apply to other infectious diseases caused by polymorphic pathogens.
authors.affiliation: Modelling and Economics Unit, Department of Statistics, Modelling and Economics, Centre for Infectious Disease Surveillance and Control, Public Health England, London, United Kingdom.|Medical Research Council Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College School of Public Health, London, United Kingdom.
authors.forename: Xu-Sheng
authors.initials: XS
authors.lastname: Zhang
mesh_terms: D060085:Coinfection / Q000453:epidemiology / Q000276:immunology* / Q000821:virology; D004196:Disease Outbreaks; D006801:Humans; D015994:Incidence; D009980:Influenza A virus / Q000145:classification / Q000276:immunology; D007251:Influenza, Human / Q000453:epidemiology / Q000276:immunology / Q000821:virology; D018448:Models, Immunological; D013045:Species Specificity; D014777:Virus Diseases / Q000453:epidemiology / Q000276:immunology* / Q000821:virology; D014780:Viruses / Q000145:classification / Q000276:immunology*