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Research Article |

Bayesian Spatio-Temporal Models for the Incidence of Malaria Using Time Dependent Covariates

This research study focuses on the Spatial and temporal Modelling of malaria incidences in Kenya, taking into account Time- dependent covariates. Malaria remains a significant public health concern in Kenya, with varying rates of infection across its 47 counties. Environmental factors such as temperature, rainfall, humidity and elevation play a crucial role in influencing Malaria transmission. Despite numerous malaria control efforts and initiatives the burden of the disease persist. The main objective of this study was to formulate Bayesian Spatio-temporal models for malaria incidence, with a particular emphasis on incorporating time-dependent covariates. The availability of data collected over time from various counties, as provided by the malaria project Atlas, was essential for achieving this goal. The Besag-York-Molli ́e (BYM) Spatio-temporal Model were formulated and implemented using Bayesian approach. Bayesian inference technique, coupled with Markov Chain Monte Carlo (MCMC) algorithms, was used to fit the models to the data. We also conducted convergence diagnostic of MCMC algorithm in order to check if the algorithm has converged and how reliable the posterior estimates are. In the analysis under Bayesian model choice and comparison of spatio-temporal model, spatial model with time dependent covariates and Spatio-temporal model with time dependent covariate were fitted. We found out that Spatio-temporal model with Time Dependent covariates was the best model. The resulting model and maps will be valuable for identifying disease hotspots, allocating resources for disease prevention and mitigation, and guiding policy decisions to reduce the burden of malaria. To ensure the validity of the Bayesian analysis, MCMC diagnostics were applied, including the Geweke Test, Gelman-Rubin statistics, and trace plots. These tests confirmed that the MCMC chains had converged to a common distribution, indicating the reliability of the obtained results.

Spatial Model, Spatio-Temporal Model, MCMC Convergence, Gelman Rubins Statistics, Malaria-Incidences, Geweke Test

APA Style

Nduvi Musyoka, E., Mwalili, S., Malenje, B. (2023). Bayesian Spatio-Temporal Models for the Incidence of Malaria Using Time Dependent Covariates. International Journal of Data Science and Analysis, 9(3), 60-66.

ACS Style

Nduvi Musyoka, E.; Mwalili, S.; Malenje, B. Bayesian Spatio-Temporal Models for the Incidence of Malaria Using Time Dependent Covariates. Int. J. Data Sci. Anal. 2023, 9(3), 60-66. doi: 10.11648/j.ijdsa.20230903.12

AMA Style

Nduvi Musyoka E, Mwalili S, Malenje B. Bayesian Spatio-Temporal Models for the Incidence of Malaria Using Time Dependent Covariates. Int J Data Sci Anal. 2023;9(3):60-66. doi: 10.11648/j.ijdsa.20230903.12

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Besag, J., York, J., and Molli ́e, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the institute of statistical mathematics, 43: 1–20.
2. Congdon, P. D. (2010). Applied Bayesian hierarchical methods. CRC Press.
3. Elagali, A., Ahmed, A., Makki, N., Ismail, H., Ajak, M., Alene, K. A., Weiss, D. J., Mohammed, A. A., Abubakr, M., Cameron, E., et al. (2022). Spatiotemporal mapping of malaria incidence in sudan using routine surveillance data. Scientific Reports, 12(1): 1–13.
4. Gelman, A. and Rubin, D. B. (1996). Markov chain monte carlo methods in biostatistics. Statistical methods in medical research, 5(4): 339–355.
5. Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. Bayesian statistics, 4: 641–649.
6. Liu, Q., Jing, W., Kang, L., Liu, J., and Liu, M. (2021). Trends of the global, regional and national incidence of malaria in 204 countries from 1990 to 2019 and implications for malaria prevention. Journal of Travel Medicine, 28(5): taab046.
7. Margaritella, N. (2020). Parameter clustering in bayesian functional pca of neuroscientific data.
8. Nkiruka, O., Prasad, R., and Clement, O. (2021). Prediction of malaria incidence using climate variability and machine learning. Informatics in Medicine Unlocked, 22: 100508.
9. Organization, W. H. et al. (2022). World malaria report 2022. World Health Organization.
10. Osnas, E. E., Heisey, D. M., Rolley, R. E., and Samuel, M. D. (2009). Spatial and temporal 57 patterns of chronic wasting disease: fine-scale mapping of a wildlife epidemic in wisconsin. Ecological Applications, (5): 1311–1322.
11. Otambo, W. O., Onyango, P. O., Ochwedo, K., Olumeh, J., Onyango, S. A., Orondo, P., Atieli, H., Lee, M.-C., Wang, C., Zhong, D., et al. (2022). Clinical malaria incidence and health seeking pattern in geographically heterogeneous landscape of western kenya. BMC Infectious Diseases, 22(1): 768.
12. Robert, C. and Casella, G. (2011). A short history of mcmc: Subjective recollections from incomplete data. Handbook of markov chain monte carlo, 49.
13. Saxena, R., Nagpal, B., Srivastava, A., Gupta, S., and Dash, A. (2009). Application of spatial technology in malaria research & control: some new insights. Indian Journal of Medical Research, 130(2): 125–132.
14. Schr ̈odle, B. and Held, L. (2011). Spatio-temporal disease mapping using inla. Environ-metrics, 22(6): 725–734.
15. Thomson, M. C. and Connor, S. J. (2001). The development of malaria early warning systems for africa. Trends in parasitology, 17(9): 438–445.
16. Were, V., Buff, A. M., Desai, M., Kariuki, S., Samuels, A., Phillips-Howard, P., Ter Kuile, F. O., Kachur, S., and Niessen, L. W. (2019). Trends in malaria prevalence and health 58 related socioeconomic inequality in rural western kenya: results from repeated household malaria cross-sectional surveys from 2006 to 2013. BMJ open, 9(9): e03388.