Predictability of epidemic malaria under non-stationary conditions with process-based models combining epidemiological updates and climate variability

Manojit Roy, Menno Bouma, Ramesh C. Dhiman, Mercedes Pascual

Previous studies have demonstrated the feasibility of early-warning systems for epidemic malaria informed by climate variability. Whereas modelling approaches typically assume stationary conditions, epidemiological systems are characterized by changes in intervention measures over time, at scales typically longer than inter-epidemic periods. These trends in control efforts preclude simple application of early-warning systems validated by retrospective surveillance data; their effects are also difficult to distinguish from those of climate variability itself. Rainfall-driven transmission models for falciparum and vivax malaria are fitted to long-term retrospective surveillance data from four districts in northwest India. Maximum-likelihood estimates (MLEs) of model parameters are obtained for each district via a recently introduced iterated filtering method for partially observed Markov processes. The resulting MLE model is then used to generate simulated yearly forecasts in two different ways, and these forecasts are compared with more recent (out-of-fit) data. In the first approach, initial conditions for generating the predictions are repeatedly updated on a yearly basis, based on the new epidemiological data and the inference method that naturally lends itself to this purpose, given its time-sequential application. In the second approach, the transmission parameters themselves are also updated by refitting the model over a moving window of time. Application of these two approaches to examine the predictability of epidemic malaria in the different districts reveals differences in the effectiveness of intervention for the two parasites, and illustrates how the 'failure' of predictions can be informative to evaluate and quantify the effect of control efforts in the context of climate variability. The first approach performs adequately, and sometimes even better than the second one, when the climate remains the major driver of malaria dynamics, as found for Plasmodium vivax for which an effective clinical intervention is lacking. The second approach offers more skillful forecasts when the dynamics shift over time, as is the case of Plasmodium falciparum in recent years with declining incidence under improved control. Predictive systems for infectious diseases such as malaria, based on process-based models and climate variables, can be informative and applicable under non-stationary conditions.