Is a reproduction number of one a threshold for Plasmodium falciparum malaria elimination?. (December 2016) - Griffin, Jamie
Abstract Background 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 ifR 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 reducedR 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 ofPlasmodium falciparum malaria in Africa. Results 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 thatR 0 is below 1 for long enough, then malaria will be locally eliminated. Conclusions This means that calculations of the reduction inR 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.