Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya

Polycarp Okiagera Nyabuto; Anthony Wanjoya; Thomas Mageto; Anthony Ngunyi

doi:doi:10.11648/j.sjams.20261401.15

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Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya

Polycarp Okiagera Nyabuto^*

, Anthony Wanjoya

, Thomas Mageto

, Anthony Ngunyi

Published in Science Journal of Applied Mathematics and Statistics (Volume 14, Issue 1)

Received: 7 December 2025 Accepted: 22 December 2025 Published: 20 January 2026

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Abstract

In Kenya, malaria remains a major public health challenge, affecting a substantial proportion of the population and exhibiting pronounced spatial and temporal variability in transmission patterns. A comprehensive understanding of the spatial and temporal distribution of malaria incidence and mortality is therefore essential for the design and implementation of effective, targeted intervention strategies aimed at reducing disease burden and preventing malaria-related deaths. This study aimed to develop and apply a Multivariate Bayesian Spatio-Temporal modeling framework incorporating skew distributions to jointly analyze the spatio-temporal distribution of malaria incidence and mortality in Kenya. This proposed approach allowed for the explicit characterization of shared spatial structures and temporal trends, as well as the dependence between incidence and mortality across different counties and time periods. Parameter estimation was conducted using the Markov Chain Monte Carlo (MCMC) algorithm, which enabled sampling from the posterior distributions and facilitated robust statistical inference under uncertainty. The performance of the proposed model was assessed using established Bayesian model evaluation criteria which included the Widely Applicable Information Criterion (WAIC), the log pointwise predictive density (lppd), and the effective number of parameters (pWAIC). These metrics were used to evaluate model fit, predictive accuracy, and complexity, ensuring a balanced assessment of model performance. The results indicated that the multivariate Bayesian spatio-temporal model effectively captured the underlying spatial and temporal dependencies in malaria incidence and mortality across Kenya. The model successfully identified variations in risk across the Kenyan Counties and time periods, demonstrating its capacity to represent intricate malaria dynamics. Thus, this study findings highlight the utility of multivariate Bayesian spatio-temporal modeling as a powerful tool for understanding malaria transmission patterns and for informing evidence-based, spatially targeted malaria control and prevention strategies in Kenya.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 14, Issue 1)
DOI	10.11648/j.sjams.20261401.15
Page(s)	37-48
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Bayesian, Multivariate, Spatial, Spatio-Temporal, Malaria Incidence, Malaria Mortality

References

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Nyabuto, P. O., Wanjoya, A., Mageto, T., Ngunyi, A. (2026). Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya. Science Journal of Applied Mathematics and Statistics, 14(1), 37-48. https://doi.org/10.11648/j.sjams.20261401.15

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ACS Style

Nyabuto, P. O.; Wanjoya, A.; Mageto, T.; Ngunyi, A. Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya. Sci. J. Appl. Math. Stat. 2026, 14(1), 37-48. doi: 10.11648/j.sjams.20261401.15

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AMA Style

Nyabuto PO, Wanjoya A, Mageto T, Ngunyi A. Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya. Sci J Appl Math Stat. 2026;14(1):37-48. doi: 10.11648/j.sjams.20261401.15

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@article{10.11648/j.sjams.20261401.15,
  author = {Polycarp Okiagera Nyabuto and Anthony Wanjoya and Thomas Mageto and Anthony Ngunyi},
  title = {Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya
},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {14},
  number = {1},
  pages = {37-48},
  doi = {10.11648/j.sjams.20261401.15},
  url = {https://doi.org/10.11648/j.sjams.20261401.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20261401.15},
  abstract = {In Kenya, malaria remains a major public health challenge, affecting a substantial proportion of the population and exhibiting pronounced spatial and temporal variability in transmission patterns. A comprehensive understanding of the spatial and temporal distribution of malaria incidence and mortality is therefore essential for the design and implementation of effective, targeted intervention strategies aimed at reducing disease burden and preventing malaria-related deaths. This study aimed to develop and apply a Multivariate Bayesian Spatio-Temporal modeling framework incorporating skew distributions to jointly analyze the spatio-temporal distribution of malaria incidence and mortality in Kenya. This proposed approach allowed for the explicit characterization of shared spatial structures and temporal trends, as well as the dependence between incidence and mortality across different counties and time periods. Parameter estimation was conducted using the Markov Chain Monte Carlo (MCMC) algorithm, which enabled sampling from the posterior distributions and facilitated robust statistical inference under uncertainty. The performance of the proposed model was assessed using established Bayesian model evaluation criteria which included the Widely Applicable Information Criterion (WAIC), the log pointwise predictive density (lppd), and the effective number of parameters (pWAIC). These metrics were used to evaluate model fit, predictive accuracy, and complexity, ensuring a balanced assessment of model performance. The results indicated that the multivariate Bayesian spatio-temporal model effectively captured the underlying spatial and temporal dependencies in malaria incidence and mortality across Kenya. The model successfully identified variations in risk across the Kenyan Counties and time periods, demonstrating its capacity to represent intricate malaria dynamics. Thus, this study findings highlight the utility of multivariate Bayesian spatio-temporal modeling as a powerful tool for understanding malaria transmission patterns and for informing evidence-based, spatially targeted malaria control and prevention strategies in Kenya.
},
 year = {2026}
}

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TY  - JOUR
T1  - Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya

AU  - Polycarp Okiagera Nyabuto
AU  - Anthony Wanjoya
AU  - Thomas Mageto
AU  - Anthony Ngunyi
Y1  - 2026/01/20
PY  - 2026
N1  - https://doi.org/10.11648/j.sjams.20261401.15
DO  - 10.11648/j.sjams.20261401.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 37
EP  - 48
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20261401.15
AB  - In Kenya, malaria remains a major public health challenge, affecting a substantial proportion of the population and exhibiting pronounced spatial and temporal variability in transmission patterns. A comprehensive understanding of the spatial and temporal distribution of malaria incidence and mortality is therefore essential for the design and implementation of effective, targeted intervention strategies aimed at reducing disease burden and preventing malaria-related deaths. This study aimed to develop and apply a Multivariate Bayesian Spatio-Temporal modeling framework incorporating skew distributions to jointly analyze the spatio-temporal distribution of malaria incidence and mortality in Kenya. This proposed approach allowed for the explicit characterization of shared spatial structures and temporal trends, as well as the dependence between incidence and mortality across different counties and time periods. Parameter estimation was conducted using the Markov Chain Monte Carlo (MCMC) algorithm, which enabled sampling from the posterior distributions and facilitated robust statistical inference under uncertainty. The performance of the proposed model was assessed using established Bayesian model evaluation criteria which included the Widely Applicable Information Criterion (WAIC), the log pointwise predictive density (lppd), and the effective number of parameters (pWAIC). These metrics were used to evaluate model fit, predictive accuracy, and complexity, ensuring a balanced assessment of model performance. The results indicated that the multivariate Bayesian spatio-temporal model effectively captured the underlying spatial and temporal dependencies in malaria incidence and mortality across Kenya. The model successfully identified variations in risk across the Kenyan Counties and time periods, demonstrating its capacity to represent intricate malaria dynamics. Thus, this study findings highlight the utility of multivariate Bayesian spatio-temporal modeling as a powerful tool for understanding malaria transmission patterns and for informing evidence-based, spatially targeted malaria control and prevention strategies in Kenya.

VL  - 14
IS  - 1
ER  -

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Author Information

Polycarp Okiagera Nyabuto

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Science and Technology, Nairobi, Kenya

Contact Email

http://orcid.org/0000-0001-5740-2674
Anthony Wanjoya

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Science and Technology, Nairobi, Kenya

Contact Email

http://orcid.org/0009-0009-7609-4318
Thomas Mageto

Department of Statistics and Actuarial Science, Jomo Kenyatta University of Science and Technology, Nairobi, Kenya

Contact Email

http://orcid.org/0009-0008-6195-041X
Anthony Ngunyi

Department of Statistics and Actuarial Science, Dedan Kimathi University of Technology, Nyeri, Kenya

Contact Email

http://orcid.org/0009-0002-1089-6392

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APA Style

Nyabuto, P. O., Wanjoya, A., Mageto, T., Ngunyi, A. (2026). Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya. Science Journal of Applied Mathematics and Statistics, 14(1), 37-48. https://doi.org/10.11648/j.sjams.20261401.15

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ACS Style

Nyabuto, P. O.; Wanjoya, A.; Mageto, T.; Ngunyi, A. Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya. Sci. J. Appl. Math. Stat. 2026, 14(1), 37-48. doi: 10.11648/j.sjams.20261401.15

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AMA Style

Nyabuto PO, Wanjoya A, Mageto T, Ngunyi A. Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya. Sci J Appl Math Stat. 2026;14(1):37-48. doi: 10.11648/j.sjams.20261401.15

Copy | Download

@article{10.11648/j.sjams.20261401.15,
  author = {Polycarp Okiagera Nyabuto and Anthony Wanjoya and Thomas Mageto and Anthony Ngunyi},
  title = {Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya
},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {14},
  number = {1},
  pages = {37-48},
  doi = {10.11648/j.sjams.20261401.15},
  url = {https://doi.org/10.11648/j.sjams.20261401.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20261401.15},
  abstract = {In Kenya, malaria remains a major public health challenge, affecting a substantial proportion of the population and exhibiting pronounced spatial and temporal variability in transmission patterns. A comprehensive understanding of the spatial and temporal distribution of malaria incidence and mortality is therefore essential for the design and implementation of effective, targeted intervention strategies aimed at reducing disease burden and preventing malaria-related deaths. This study aimed to develop and apply a Multivariate Bayesian Spatio-Temporal modeling framework incorporating skew distributions to jointly analyze the spatio-temporal distribution of malaria incidence and mortality in Kenya. This proposed approach allowed for the explicit characterization of shared spatial structures and temporal trends, as well as the dependence between incidence and mortality across different counties and time periods. Parameter estimation was conducted using the Markov Chain Monte Carlo (MCMC) algorithm, which enabled sampling from the posterior distributions and facilitated robust statistical inference under uncertainty. The performance of the proposed model was assessed using established Bayesian model evaluation criteria which included the Widely Applicable Information Criterion (WAIC), the log pointwise predictive density (lppd), and the effective number of parameters (pWAIC). These metrics were used to evaluate model fit, predictive accuracy, and complexity, ensuring a balanced assessment of model performance. The results indicated that the multivariate Bayesian spatio-temporal model effectively captured the underlying spatial and temporal dependencies in malaria incidence and mortality across Kenya. The model successfully identified variations in risk across the Kenyan Counties and time periods, demonstrating its capacity to represent intricate malaria dynamics. Thus, this study findings highlight the utility of multivariate Bayesian spatio-temporal modeling as a powerful tool for understanding malaria transmission patterns and for informing evidence-based, spatially targeted malaria control and prevention strategies in Kenya.
},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Multivariate Bayesian Spatio-Temporal Modeling of Malaria Incidence and Mortality in Kenya

AU  - Polycarp Okiagera Nyabuto
AU  - Anthony Wanjoya
AU  - Thomas Mageto
AU  - Anthony Ngunyi
Y1  - 2026/01/20
PY  - 2026
N1  - https://doi.org/10.11648/j.sjams.20261401.15
DO  - 10.11648/j.sjams.20261401.15
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 37
EP  - 48
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20261401.15
AB  - In Kenya, malaria remains a major public health challenge, affecting a substantial proportion of the population and exhibiting pronounced spatial and temporal variability in transmission patterns. A comprehensive understanding of the spatial and temporal distribution of malaria incidence and mortality is therefore essential for the design and implementation of effective, targeted intervention strategies aimed at reducing disease burden and preventing malaria-related deaths. This study aimed to develop and apply a Multivariate Bayesian Spatio-Temporal modeling framework incorporating skew distributions to jointly analyze the spatio-temporal distribution of malaria incidence and mortality in Kenya. This proposed approach allowed for the explicit characterization of shared spatial structures and temporal trends, as well as the dependence between incidence and mortality across different counties and time periods. Parameter estimation was conducted using the Markov Chain Monte Carlo (MCMC) algorithm, which enabled sampling from the posterior distributions and facilitated robust statistical inference under uncertainty. The performance of the proposed model was assessed using established Bayesian model evaluation criteria which included the Widely Applicable Information Criterion (WAIC), the log pointwise predictive density (lppd), and the effective number of parameters (pWAIC). These metrics were used to evaluate model fit, predictive accuracy, and complexity, ensuring a balanced assessment of model performance. The results indicated that the multivariate Bayesian spatio-temporal model effectively captured the underlying spatial and temporal dependencies in malaria incidence and mortality across Kenya. The model successfully identified variations in risk across the Kenyan Counties and time periods, demonstrating its capacity to represent intricate malaria dynamics. Thus, this study findings highlight the utility of multivariate Bayesian spatio-temporal modeling as a powerful tool for understanding malaria transmission patterns and for informing evidence-based, spatially targeted malaria control and prevention strategies in Kenya.

VL  - 14
IS  - 1
ER  -

Copy | Download