Fig 1.
Location of the population-based infectious disease surveillance (PBIDS) area in western Kenya. The inset (top right) shows the position of the PBIDS study area within Kenya (red dot). The main panel displays the 10 clusters (IDs 1–10) used for analysis and the location of Lwak Mission Hospital within the study area. These maps were created using the tmap-package in R, and the basemap shapefiles were downloaded from ESPEN (2022) (https://espen.afro.who.int/maps-data/data-query-tools/cartography-database and https://data.humdata.org/dataset/cod-ab-ken).
Fig 2.
Diagram of the compartmental structure of the model.
For each cluster u, the human population is divided into five classes: - susceptible to infection;
- exposed to parasites that have not yet matured into gametocytes;
- infected with symptoms and infectious;
- asymptomatic with reduced parasitemia; and
- recovered and protected from severe infection. Transitions between the human compartments are denoted by a solid arrow with rate μ, and transitions between the human and mosquito compartments are denoted by dotted lines. The chain of compartments
implements a distributed time delay between infections in humans and the force of infection (the per-capita rate of infection) experienced by a susceptible individual, as described in Methods Section. The model is formalized by the stochastic differential equations (3)-(7).
Fig 3.
Reporting rates (in %) per cluster I-X.
Estimated reporting rates () from the best-fitting model. Left: spatial distribution of reporting rates across clusters. Right: relationship between cluster distance to Lwak Mission Hospital and reporting rate. The base map is derived from population-based infectious disease surveillance (PBIDS) shapefiles provided by the Kenya Medical Research Institute (KEMRI). The map was generated in R (version 4.4.2) using the ggplot2 package.
Fig 4.
Observed monthly malaria cases are shown in red. The median of 1000 simulations from the best-fitting model is shown in blue, with prediction uncertainty represented by the 10 - 90% quantiles (shaded blue).
Fig 5.
Malaria forecasts per cluster I-X.
Observed monthly malaria cases are shown in red. The median of 1000 simulations from the best-fitting model is shown in blue, with prediction uncertainty (10 - 90% quantiles) shaded blue. Forecasted incidence for 2020 - 2022 is shown in cyan, with forecast uncertainty (10 - 90% quantiles) shaded in cyan.
Fig 6.
Diagrammatic representation of a spatio-temporal partially observed Markov process. The value of the latent process at time is denoted by
, and the partial and noisy observations are modeled by
, where there are U units labeled
.