Fun with Maths: Exploring Implications of Mathematical Models for Malaria Eradication

December 11, 2014

Abstract: 

Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.

This figure shows the difference in the probability of infections lasting less than 90 days for an exponential distribution and a log normal distribution.

The difference in remaining distribution of infection duration following a 90-day case detection lag for an exponential distribution (blue) and a log-normal distribution (green), each with a mean of 180 days.

Conclusions In summary, the example demonstrates the power of data-driven mathematical analyses for informing malaria eradication strategy. Mathematical modeling forces one to make assumptions explicit and reveals the implications of those assumptions.