Is a reproduction number of one a threshold for Plasmodium falciparum malaria elimination?

Jamie T. Griffin

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.