Is Elimination Sticky?
Should Malaria Policy Depend on Backwards Bifurcations
Draft – I’m looking for co-authors. Let me know if you’re interested in helping me write this.
The mathematical support for malaria eradication – the idea that malaria could be pulled up by the roots and never return – was never supported by the mathematics. Macdonald’s models all suggested that malaria should be globally stable – if conditions didn’t change, then after the reintroduction of malaria, it would return to a stable, endemic equilibrium. Macdonald’s model ignored malaria immunity, spatial dynamics, heterogeneity, stochasticity, and many other aspects of malaria that would affect the answer to the question. Perhaps this is the reason why mathematical models played a minor role in the design of the Global Malaria Eradication Programme. In fact, malaria elimination ended up becoming a stable endpoint for many countries [1,2]. In other countries, the failure to finish the job meant malaria would become resurgent [3].
This essay explores the mathematical theory developed since Macdonald. The question is whether malaria elimination could be a stable endpoint. One idea is called a backwards bifurcation [4].
Heterogeneity
If malaria transmission is heterogeneous over space and time, then in some systems where malaria would persist in deterministic models – because the dominant eigenvalue is positive – the probability of establishing depends on the way malaria gets introduced into the system. If most of the sub-dominant eignvalues are negative, then malaria will tend to decline when it is first introduced. In practical terms, this enhance the stability of malaria elimination.
Health Systems
In areas where malaria immunity has waned, most cases of malaria would cause disease, prompt health seeking,
Outbreak Response
In areas where malaria elimination has been