Malaria is one of the most common diseases in the sub-Saharan Africa. The purpose of this study is to estimate the transitioning probabilities of initial infection from Healthy or Uncomplicated to Severe State form and vice versa. It also classifies the various transitioning probabilities of moving through the various states based on some baseline characteristics. Malaria test results for 2019 over a 12-month period were collected from the University of Ghana school clinic. An H-U model for the study was developed and the transition rates from the cross-sectional data are indicated. With two states Healthy (H) and Uncomplicated (U) forming a state space, there were four possible transitions. The results show that the probability of transitioning from the Healthy state to the malaria positive state is 0.03% while the probability that an individual will remain at Healthy state (H) after the test is 99.73%. We recommend a more enhanced sensitization measure on the need to prevent malaria parasite on campuses.

malaria model, transition matrix, Markov chain, malaria statistics.

Received: December 2, 2020; Revised: August 21, 2021; Accepted: September 18, 2021; Published:  October 20, 2021

How to cite this article: Dennis Arku, Gabriel Kallah-Dagadu and Debrah Godwin, A stochastic H-U model for malaria transmission via markov theory, JP Journal of Biostatistics 18(3) (2021), 459-473. DOI: 10.17654/BS018010459

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

Reference:

[1] CDC, Centers for Disease Central and Prevention, Retrieved from Centers for disease Central and Prevention, 2019.
https://www.cdc.gov/malaria/about/disease.html.
[2] L. A. Goodman, Statistical Inference about Markov Chains, 2014. https://doi.org/10.1214/aoms/1177707039.
[3] C. O. Odongo, K. R. Bisaso, F. Kitutu, C. Obua and J. Byamugisha, Is there a distinction between malaria treatment and intermittent preventive treatment? Insights from a cross-sectional study of anti-malarial drug use among Ugandan pregnant women, Malaria Journal 14(1) (2015), 1-9. https://doi.org/10.1186/s12936-015-0702-7.
[4] J. Nedelman, Introductory review some new thoughts about some old malaria models, Mathematical Biosciences 73(2) (1985), 159-182.
https://doi.org/10.1016/0025-5564(85)90010-0.
[5] A. Richard, S. Richardson and J. Maccario, A three-state Markov model of Plasmodium falciparum parasitemia, Mathematical Biosciences 117(1-2) (1993), 283-300. https://doi.org/10.1016/0025-5564(93)90029-A.
[6] M. Sandip, R. S. Ram and S. Somdatata, Mathematical modelling of malaria - a review, Malaria Journal 10 (2011), Article number 202. Retrieved from: https://malariajournal.biomedcentral.com/articles/10.1186/1475-2875-10-202.
[7] Severe Malaria Observatory, Severe Malaria Observatory, Retrieved from Severe Malaria Observatory, 2019. Website: https://www.severemalaria.org/countries/ghana.
[8] F. A. Sonnenberg, J. R. Beck, A. Frank and J. R. Beck, Markov Models in Medical Decision Making : A Practical Guide, 1993. https://doi.org/10.1177/0272989X9301300409.
[9] C. Twumasi, L. Asiedu and E. N. N. Nortey, Markov chain modeling of HIV, tuberculosis, and hepatitis B Transmission in Ghana, Interdisciplinary Perspectives on Infectious Diseases 2019 (2019), 1-8. https://doi.org/10.1155/2019/9362492.
[10] WHO, World Health Organization, Retrieved from World Health Organization, 2019. Website: https://www.who.int/malaria/areas/treatment/en/.
[11] WHO, World Health Organization, Retrieved from World Health Organization 2019. Website: https://www.who.int/news-room/fact-sheets/detail/malaria.