Vector-borne infectious disease mapping with stochastic difference equations: an analysis of dengue disease in Malaysia

Few publications consider the estimation of relative risk for vector-borne infectious diseases. Most of these articles involve exploratory analysis that includes the study of covariates and their effects on disease distribution and the study of geographic information systems to integrate patient-related information. The aim of this paper is to introduce an alternative method of relative risk estimation based on discrete time– space stochastic SIR-SI models (susceptible–infective–recovered for human populations; susceptible– infective for vector populations) for the transmission of vector-borne infectious diseases, particularly dengue disease. First, we describe deterministic compartmental SIR-SI models that are suitable for dengue disease transmission. We then adapt these to develop corresponding discrete time–space stochastic SIRSI models. Finally, we develop an alternative method of estimating the relative risk for dengue disease mapping based on these models and apply them to analyse dengue data from Malaysia. This new approach offers a better model for estimating the relative risk for dengue disease mapping compared with the other common approaches, because it takes into account the transmission process of the disease while allowing for covariates and spatial correlation between risks in adjacent regions.