Quantifying multivariate spatio-temporal dynamics of malaria risk by multiple Plasmodium species using graph-based optimization in Southern Ethiopia

Although malaria incidence has fallen sharply over the past few years, the rate of decline varies by district, time, and malaria type and has recently shown a signal of re-emergence. Modelling such dynamics has a significant impact on people’s health, especially those in lower-resource settings. Most studies estimate such inequalities based solely on P. falciparum. Thus, the present study aims to develop a predictive model that helps to identify the spatio-temporal variation in malaria risk by multiple Plasmodium species. Multivariate spatio-temporal models were proposed to better capture the distribution of disease risk across incidences and change over time. The spatial autocorrelation in such occasions is typically modelled by a set of random effects that assign a conditional autoregressive prior distribution. However, the autocorrelation considered in such cases depends on a binary neighbourhood matrix specified through the border-sharing rule. Over here, we propose a graph-based optimization algorithm (GBOA) for estimating the neighbourhood matrix that merely represents the spatial correlation by exploring the areal units as the vertices of a graph and the neighbour relations as the series of edges. From the results of the analysis, precipitation, temperature, and humidity are positively associated with the malaria threat in the area. On the other hand, enhanced vegetation index, nighttime light (NTL), and distance from coastal areas are negatively associated. Moreover, nonlinear relationships were observed between malaria incidence and precipitation, temperature, and NTL. Additionally, lagged effects of temperature and humidity have a significant effect on malaria risk by either species. More elevated risk of P. falciparum was observed following the rainy season, and unstable transmission of P. vivax was observed in the area. Finally, P. vivax risks are less sensitive to environmental risks than that of P. falciparum. A more accurate inference can then be made by using GBOA via removing planar graph edges resulting from border-sharing across geographic regions, in comparison to the commonly used border-sharing rule. Additionally, elevated risks of either of the cases were observed in districts found in the central and western regions. As malaria transmission operates spatially continuously, a spatially continuous model should be employed when it is computationally feasible.