title: Is a reproduction number of one a threshold for Plasmodium falciparum malaria elimination?
abstract: The basic reproduction number (R 0) is an important summary of the dynamics of an infectious disease. It is a threshold parameter: an infection can only invade a population if R 0 is greater than 1. However, a number of studies using simple models have suggested that for malaria, it is in theory possible for infection to persist indefinitely even if an intervention has reduced R 0 below 1. Such behaviour is known as a bistable equilibrium. Using two published mathematical models which have both been fitted to detailed, age-stratified data on multiple outcomes, the article investigates whether these more complex models behave in such a way, and hence whether a bistable equilibrium might be a real feature of Plasmodium falciparum malaria in Africa.
  
  
  
  With the best-fitting parameter values, neither model has a bistable state, because immunity reduces onwards infectiousness. The results imply that there is a threshold such that if interventions can reduce transmission so that R 0 is below 1 for long enough, then malaria will be locally eliminated.
  
  
  
  This means that calculations of the reduction in R 0 that interventions can achieve (the effect size) have a useful and straightforward interpretation, whereas if the theoretical possibility of a bistable equilibrium were the real behaviour, then such effect size calculations would not have a clear interpretation.
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK. j.griffin@qmul.ac.uk.
authors.forename: Jamie T
authors.initials: JT
authors.lastname: Griffin
mesh_terms: D000349:Africa / Q000453:epidemiology; D050936:Basic Reproduction Number; D060740:Disease Eradication; D018562:Disease Transmission, Infectious; D006801:Humans; D016778:Malaria, Falciparum / Q000453:epidemiology / Q000517:prevention & control* / Q000635:transmission*; D015233:Models, Statistical
keywords: Elimination; Malaria; Mathematical model; Reproduction number