title: Estimation of a time-varying force of infection and basic reproduction number with application to an outbreak of classical swine fever.
abstract: BACKGROUND
  A method was developed for stochastically reconstructing the pattern of infection from observed epidemic data. This allowed for estimation of a time-dependent force of infection, or transmission rate, during an epidemic.
  
  
  METHODS
  A discrete-time mechanistic model was used to describe the spread of infection and a stochastic procedure, which utilised the latent and infectious period distributions, was used to reconstruct the dates of infection, becoming infectious and removal from the given data. The four equations describing the model were then solved to obtain least squares estimates of the transmission rate and the basic reproduction number (R0) throughout the epidemic. This process was repeated in order to assess the variability in these key epidemiological parameters. The stochastic epidemic reconstruction procedure was developed to account for changes in the distribution of the survival period over the course of the epidemic and adapted for application to epidemic data where not all infected individuals have yet been observed as cases.
  
  
  RESULTS
  The method was applied to a set of epidemic data from an outbreak of classical swine fever in Pakistan. Constant and time-varying estimates of the transmission rate were derived and compared. There was some evidence to suggest that the force of infection varied over time.
  
  
  CONCLUSIONS
  The method described can be applied to data from epidemics where observations are incomplete. The confidence limits obtained for the estimated force of infection provide a means of assessing the evidence for time variation in this parameter.
authors.affiliation: Wellcome Trust Centre for the Epidemiology of Infectious Disease, Department of Zoology, University of Oxford, UK.
authors.forename: S C
authors.initials: SC
authors.lastname: Howard
authors.forename: C A
authors.initials: CA
authors.lastname: Donnelly
mesh_terms: D000818:Animals; D000835:Animals, Wild; D006691:Classical Swine Fever / Q000401:mortality / Q000635:transmission*; D016001:Confidence Intervals; D004196:Disease Outbreaks / Q000706:statistics & numerical data / Q000662:veterinary*; D016018:Least-Squares Analysis; D008954:Models, Biological; D010154:Pakistan / Q000453:epidemiology; D013269:Stochastic Processes; D016019:Survival Analysis; D013552:Swine; D013997:Time Factors