The role of simple mathematical models in malaria elimination strategy design

Malaria has recently been identified as a candidate for global eradication. This process will take the form of a series of national eliminations. Key issues must be considered specifically for elimination strategy when compared to the control of disease. Namely the spread of drug resistance, data scarcity and the adverse effects of failed elimination attempts. Mathematical models of various levels of complexity have been produced to consider the control and elimination of malaria infection. If available, detailed data on malaria transmission (such as the vector life cycle and behaviour, human population behaviour, the acquisition and decay of immunity, heterogeneities in transmission intensity, age profiles of clinical and subclinical infection) can be used to populate complex transmission models that can then be used to design control strategy. However, in many malaria countries reliable data are not available and policy must be formed based on information like an estimate of the average parasite prevalence.

A simple deterministic model, that requires data in the form of a single estimate of parasite prevalence as an input, is developed for the purpose of comparison with other more complex models. The model is designed to include key aspects of malaria transmission and integrated control.

The simple model is shown to have similar short-term dynamic behaviour to three complex models. The model is used to demonstrate the potential of alternative methods of delivery of controls. The adverse effects on clinical infection and spread of resistance are predicted for failed elimination attempts. Since elimination strategies present an increased risk of the spread of drug resistance, the model is used to demonstrate the population level protective effect of multiple controls against this very serious threat.

A simple model structure for the elimination of malaria is suitable for situations where data are sparse yet strategy design requirements are urgent with the caveat that more complex models, populated with new data, would provide more information, especially in the long-term.