Why I do it with (Mathematical) Models


Josh Havumaki

Apologies to our friends in the bio-stats department. There is a definite need for statistical methods in public health. Many of the tools that biostatisticians use are well established and necessary for things like causal inference. However, there are certain questions that aren’t sufficiently addressed by statistical techniques. Therefore, dynamic mathematical models have become more prominent in epidemiology and other branches of public health.

Here are a few public health issues that can be explored more effectively using dynamic mathematical models.

1) Figuring out the best way to vaccinate a population. If GAVI allocates enough influenza vaccine to the government of Indonesia to inoculate 10% of the population, where should the prevention efforts be focused to ensure maximal coverage (e.g. rural vs. urban populations)?

Past literature has focused on sharing the worlds vaccine or antiviral stockpile. For example, if the wealthiest countries share only a fraction of their influenza vaccines with the developing world, the effects would be much greater than expected. As the strategy becomes more cooperative, the containment efforts become more effective – even for the countries sharing their vaccine or antiviral stockpiles.

2) Building multi scale representations of how disease progresses and spreads. The beauty of dynamic modeling is in its modularity. It is possible to combine a cellular model of influenza pathology with one of transmission dynamics at the population level. This can provide information about interplay between levels.

3) The right kind of dynamic model (i.e. an agent based model) can grant insight into the stochastic (random or unpredictable) nature of pandemics. If a small influenza outbreak of occurs in Southeast Asia, what is the threshold that needs to be reached before it becomes a pandemic. This can factor in things like herd immunity and heterogeneity of susceptibility in the population due to immunity.

The major caveat is that accurate and quantitative data to validate and inform dynamic models can be difficult to find especially in lower resource countries (where many pandemics start). However, data quality is ever improving and organizations are becoming more strategic about collecting and synthesizing large amounts of information as seen in fields like health informatics.

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