Bayesian reasoning and SIR malaria models

Abstract

Various sources of uncertainty are involved in malaria modelling, arising from intricate interplay between parasite biology, vector ecology, human factors and environmental variables. These uncertainties are magnified by data constraints, the spread of drug and insecticide resistance and the difficulties associated with reliably accounting for intervention effects and long-term climate impacts. It is imperative to employ complicated statistical techniques, ensemble modelling approaches and consistently improve models as new information becomes available for purposes of offering strong guidance to public health decision-making about the inherent complexity and fluctuation in transmission dynamics of malaria. To assess the impact of intervention measures put in place, it is important to quantify the uncertainty and take it into account when making decisions. Bayesian inference makes this possible in the sense that the posterior parameter inference can characterize uncertainty in the estimates of unknown parameter values and indeed the uncertainty over a set of candidate models.
In this work, we apply Bayesian inference based on Markov chain Monte Carlo (MCMC) sampling to a compartmental models (SIR) Ross’ original model. We define a ground truth, subject it to actual data and infer the posterior distribution of the initial state and the parameters of the model. We investigate several scenarios for the observations generated corresponding to realistic situations. This way, we can contrast the inferred posterior to the ground truth and the amount of uncertainty injected in the observations.