Understanding the Dynamics of Amebiasis Using Mathematical Modelling Approach: Optimal Control Strategies and Cost-Effectiveness Analysis
Keywords:
Amebiasis, Mathematical model, Global sensitivity analysis, Optimal control, Cost-effectiveness analysis
Abstract
Amebiasis is a parasitic infection of the intestine caused by the amoeba Entamoeba histolytica and is endemic in tropical countries with poor sanitation and hygiene. To explore the dynamics of amebiasis and identify effective control interventions, a mathematical model is developed. This model incorporates a treatment class within the human population and accounts for the concentration of the amebiasis pathogen in the environment. The study derived the steady states, stability, and the basic reproduction number of the infection. A global sensitivity analysis is also conducted to identify the most significant parameters influencing the disease's spread. Subsequently, an optimal control model is formulated, featuring four time-dependent controls: hygiene practices, efficient screening of infected individuals, effective treatment, and disinfection/sterilisation of the environment. This model is analysed and simulated across four categories—single, double, triple, and quadruple combinations—to assess the impact of these control measures. Additionally, a cost-effectiveness analysis is conducted using the incremental cost-effectiveness ratio (ICER) method. The findings provide valuable insights that can help policymakers effectively control the disease while managing limited resources. The results indicate that any control combination that includes efficient screening of infected individuals is the most cost-effective strategy for reducing amebiasis in society. However, in a single case where resources are limited, Strategy 2 - efficient screening of infected individuals - emerges as the most cost-effective method for eradicating the disease. With additional resources, the most effective double-combined control strategy for disease eradication is Strategy 8, which combines Strategy 2 with efficient treatment. For the triple control strategy, the most cost-effective control Strategy is Strategy 14, which integrates Strategy 8 and disinfection/sterilisation of the environment. However, the overall most cost-effective strategy remains Strategy 2.
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Mwaijande, S. E. and Mopolo, G. E. (2022). Mathematical Modeling of The Transmission Dynamics of Amoebiasis With Some Interventions, 03 March 2022, PREPRINT (Version 1) available at Research Square [https://doi.org/10.21203/rs.3.rs-1363033/v1]
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Gwervina, R. I., Madubueze, C. E. & Kaduna, F. S. (2021). Mathematical Assessment of the Role of Denial on COVID-19 Transmission with N n-Linear Incidence and Treatment Functions. Sci Afr. 12:e00811. doi: 10.1016/j.sciaf.2021. e00811. Epub 021 Jun 14. PMID: 34151051; PMCID: PMC8200329.
Odeh, J. O., Agbata, B. C., Tijani, K. A. & Madubueze, C. E.(2024). Optimal Control Strategies for the Transmission Dynamics of Zika Virus: With the Aid of Wolbachia-Infected Mosquitoes. Numerical and Computational Methods in Sciences and Engineering. 5(1), 2024,PP: 1-25, doi:10.18576/ncmse/050101.
Tijani, K. A., Madubueze, C. E. & Gwervina, R.I. (2024). Modelling Typhoid Fever Transmission with Treatment Relapse Response: Optimal Control and Cost-Effectiveness Analysis. Math Models Comput Simul 162024, 457-485 . https://doi.org/10.1134/S2070048224700169.
Kazeem A. Tijani, Chinwendu. E. Madubueze, Isaac O. Onwubuyia, Nkiruka Maria-Assumpta Akabuike and John Olajide Akanni. (2025). Mathematical modelling of the dynamical system of military population, focusing on the impact of welfare, J. Nig. Soc. Phys. Sci. , 7 (2025) 2844, DOI:10.46481/jnsps.2025.2844.
Hategekimana, F., Saha, S., and Chaturvedi, A. (2017). Dynamics of Amoebiasis Transmission: Stability and Sensitivity Analysis. Mathematics, 5(4), 58. https://doi.org/10.3390/math5040058
Edward, S. and Mopolo, G. E. Modeling and optimal control of the transmission dynamics of amebiasis. (2023).Results in Control and Optimization,Volume 13, 2023, 100325, ISSN 2666-7207, https://doi.org/10.1016/j.rico.2023.100325.
Mpeshe, S. C. Fuzzy SEIR Epidemic Model of Amoebiasis Infection in Human. (2022). Advance in Fuzzy Systems. https://doi.org/10.1155/2022/5292830
Fidele, H., Chaturvedi, A., Snehanshu, S. and Kigali, R. Modeling The Dynamics of Amoebiasis Transmission: Case of Simultaneous Infectious States. Accessed from https://www.researchgate.net/profile/Snehanshu-Saha/publication/335223231_Modeling_The_Dynamics_of_Amoebiasis_Transmission_Case_of_Simultaneous_Infectious_States/links/5d59953392851cb74c75fea1/Modeling-The-Dynamics-of-Amoebiasis-Transmission-Case-of-Simultaneous-Infectious-States.pdf
Hategekimana, F., Saha, S.,& Chaturvedi, A. (2016). Amoebiasis Transmission and Life cycle: A continuous state description by virtue of existence and uniqueness. Global Journal of Pure and Applied Mathematics, 12(1), 375-390.
Mwaijande, S. E. and Mopolo, G. E. (2022). Mathematical Modeling of The Transmission Dynamics of Amoebiasis With Some Interventions, 03 March 2022, PREPRINT (Version 1) available at Research Square [https://doi.org/10.21203/rs.3.rs-1363033/v1]
Birkhoff, G and Rota, G. (1969). Ordinary Differential Equations, 2nd ed., Waltham, Mass.: Blaisdell Publishing Co.
Tijani, K. A., Madubueze, C. E. & Gwervina, R. I. (2023). Typhoid fever dynamical model with cost-effective optimal control. Journal of the Nigerian Society of Physical Sciences, 5(4),2023, 1579. https://doi.org/10.46481/jnsps.2023.1579
Madueme, P, U and Chirvoe, F. (2023). Understanding the transmission pathways of Lassa fever: A mathematical modeling approach. Infectious Disease Modelling, 8(2023): 27-57. https://doi.org/10.1016/j.idm.2022.11.010.
Stauffer, W. and Ravdin, J.I: Entamoeba histolytica: an update. Current opinion in infectious diseases, 16(5), 479-485(2003).
Tilahun, G. T., Oluwole, D. M. & David, M. (2017). "Modelling and Optimal Control of Typhoid Fever Disease with Cost Effective Strategies", Computations and Mathematical methods in Medicine, 2324518 (2017). https://doi.org/10.1155/2017
Encyclopedia of Mathematics, "Optimal control, mathematical theory of", (2020). Accessed on http://encyclopediaofmath.org/index.php?title=Optimal_control,_mathematical_ theory_of&oldid=48051
Lauer, J. A. Morton, A. & Bertram, M. (2019). "Cost-Effectiveness Analysis", in Ole F. Norheim, Ezekiel J. Emanuel, and Joseph Millum (eds), Global Health Priority-Setting: Beyond Cost-Effectiveness (New York, 2019; online edn, Oxford Academic, 19 Dec. 2019), https://doi.org/10.1093/oso/9780190912765.003.0005, accessed 23 Apr. 2023.
Heymann, D. L., Ed., Control of Communicable Diseases Manual, American Public Health Association, Washington DC, USA, 20 edition, 2015.
Heffernan, J. M., Smith, R. J. & Wahl, L. M. Perspectives on the Basic Reproductive Ratio. Journal of the Royal Society Interface. 2(2005): 281-293.
Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton university press, 2011.
Davis, C. P. and Balentine, J. R. (2019). "Amebiasis (Entamoeba histolytica infection)," 2019, https://www.medicinenet.com/amebiasis_entamoeba_histolytica_infection/article. htm
Van den Driessche P. and Watmough, J. (2002). Reproduction Number and Subthreshold Endemic Equilibrium for Compartmental Models of Disease Transmission. Mathematical Biosciences, 2002:29-48
Castillo-Chavez, C., Feng, Z. and Huang, W. (2002) On the Computation of RO and Its Role on Global Stability. In: Castillo-Chavez, P.C., Blower, S., Driessche, P., Kirschner, D. and Yakubu, A.-A., Eds., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer, Berlin, 229.
Lunga, M. M. (2012). Mathematical Models for the coinfection Dynamics of Cholera and Typhoid (Doctoral Thesis/Master's Dissertation). Johannesburg: University of Johannesburg. Available from: http://hdl.handle.net/102000/0002(Accessed on 20 June, 2024)
Blower, S. M. & Dowlatabadi, H. (1994). Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission : an HIV Model, as an Example. International Statistical Review, 62(1994): 229-243.
Odetunde, O., & Ibrahim, M. O. (2021). Stability Analysis of Mathematical Model of a RelapseTuberculosis Incorporating Vaccination. International Journal of Mathematical Sciences andOptimization: Theory and Applications, 7(1), 116-130.
Danbaba, U. A., Aloko, M. D., & Ayinde, A. M. (2024). Mathematical modeling of mosquito borne diseases with vertical transmissions as applied to Dengue. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(3), 31 - 56. Retrieved from https://ijmso.unilag.edu.ng/article/view/2195
Marino, S., Hogue, I. B., Ray, C. J. & Kirschner, D. E.(2008) A Methodology for Performing Global Uncertainty and Sensitivity Analysis in S stems Biology. Journal of Theoretical Biology. 254(1), 2008: 178-196.
Madubueze, C. E. Tijani, K. A. & Fatmawati. (2023) A deterministic mathematical model for optimal control of diphtheria disease with booster vaccination. Healthcare Analytics, 4(2023),100281, ISSN 2772-4425,https://doi.org/10.1016/j.health.2023.100281.
Gwervina, R. I., Madubueze, C. E., Baijya, V. P. & Esla, F. E. (2023).Modeling and Analysis of Tuberculosis and Pneumonia Co-Infection Dynamics with Cost-Effective Strategies". Results in Control and Optimization, 10(2023): 100210.
Akanni, J. O., Akinpeli, F. O. & Ogunsola, A. W. "Modelling Financial Crime Population Dynamics: Optimal Control and Cost-Effectiveness Analysis", International Journal of Dynamics and Control, 8(2020), 531-544.
Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V. and Mishchenko, E. F. "The Mathematical Theory of Optimal Processes", John Wiley & Sons, London, UK (1962).
Fleming, W. A., and Rishel, R. W. "Deterministic and Stochastic Optimal Control", Springer Verlag, New York (1975).
Asamoah, J. K. K., Okyere, E., Abidemi, A., Moore, S. E., Sun, G., Jim, Z., Acheampong, E. & Gordon, J. F. (2022). "Optimal Control and Comprehensive Cost Effectiveness for Covid 19", Results in Physics, 33(2022) 105177. https://doi.org/10.1016/j.rinp.2022.105177
Berhe, H. W., Makinde, O. D. & Thevri, D. M. (2007)."Optimal Control and Cost-Effectiveness Analysis for Dysentery Epidemic Model", International Journal of Applied Mathematics and Information Sciences, 12(6), 1183-1195 (2007). https://doi.org/10.18576/amis/120613
Published
2025-10-15
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Tijani, K. A., & Madubuzeze, C. E. (2025). Understanding the Dynamics of Amebiasis Using Mathematical Modelling Approach: Optimal Control Strategies and Cost-Effectiveness Analysis. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(3), 138 - 166. Retrieved from https://ijmso.unilag.edu.ng/article/view/2908
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