MATHEMATICAL MODELING AND OPTIMAL CONTROL ANALYSIS OF HUMAN AFRICAN TRYPANOSOMIASIS TRANSMISSION WITH RELAPSE RESPONSE
DOI:
https://doi.org/10.60787/jnamp.vol70no.567Keywords:
Compartmental model, Stability, Optimal control, Relapse, Disease eliminationAbstract
Human African Trypanosomiasis (HAT), a neglected tropical disease transmitted by tsetse flies, remains a health issue in sub-Saharan Africa. This study develops a seven-compartment mathematical model that includes human and vector dynamics, along with relapse mechanisms. The model's consistency is confirmed through boundedness and positivity analysis. Equilibrium points are calculated, and stability is discussed. The transmission potential via the basic reproduction number, R₀ was derived. An optimal control framework integrates three strategies: public awareness, regular screening and treatment, and vector control with insecticide traps. Using Pontryagin’s Principle, cost-effective approaches are identified to reduce infections. Simulations show that combined interventions effectively lower HAT prevalence, with relapse management preventing resurgence. The findings highlight the importance of coordinated, timely strategies and relapse-aware healthcare, providing valuable insights for policymakers to implement resource-efficient measures for HAT elimination.
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References
A. G. Kermack, W. O., & McKendrick, “A contribution to the math- ematical theory of epidemics,” R. Soc. london. Ser. A, vol. 115, no. 772, pp. 700–721., 1927.
J. W. V. A. Herbert W. Hethcote, Modeling HIV Transmission and AIDS in the United States. 2013.
D. S. Ferguson, N. M., Cummings, D. A., Fraser, C., Cajka, J. C., Cooley, P. C., & Burke, “Strategies for mitigating an influenza pandemic,” Nature, vol. 442, no. 7101, pp. 448–452, 2006.
C. N. Davis, M. J. Keeling, and K. S. Rock, “Modelling gambiense human African trypanosomiasis infection in villages of the Democratic Republic of Congo using Kolmogorov forward equations,” J. R. Soc. Interface, vol. 18, no. 183, 2021, doi: 10.1098/rsif.2021.0419.
K. Peter, O. J., Ibrahim, M. O., Edogbanya, H. O., Oguntolu, F. A., Oshinubi and J. O. Ibrahim, A. A., . . . Lawal, “Direct and indirect transmission of typhoid fever model with optimal control,” Results Phys., vol. 27, no. 104463, 2021.
H. A. Abioye, A. I., Ibrahim, M. O., Peter, O. J., & Ogunseye, “Optimal control on a mathematical model of malaria,” Sci. Bull., Ser. A Appl Math Phy, vol. 82, no. 3, pp. 177–190, 2020.
F. Weidemann, “Optimal control on a mathematical model of malaria,” 2015.
J. W. Hargrove, R. Ouifki, D. Kajunguri, G. A. Vale, and S. J. Torr, “Modeling the control of trypanosomiasis using trypanocides or insecticide-treated livestock,” PLoS Negl. Trop. Dis., vol. 6, no. 5, 2012, doi: 10.1371/journal.pntd.0001615.
M. Helikumi and S. Mushayabasa, “Mathematical modeling of trypanosomiasis control strategies in communities where human, cattle and wildlife interact,” Anim. Dis., vol. 3, no. 1, pp. 1–15, 2023, doi: 10.1186/s44149-023-00088-6.
H. E. Gervas and A. K. Hugo, “Modelling african trypanosomiasis in human with optimal control and cost-effectiveness analysis,” J. Appl. Math. Informatics, vol. 39, no. 5–6, pp. 895–918, 2021, doi: 10.14317/jami.2021.895.
H. E. Gervas, N. K. D. O. Opoku, and S. Ibrahim, “Mathematical Modelling of Human African Trypanosomiasis Using Control Measures,” Comput. Math. Methods Med., vol. 2018, 2018, doi: 10.1155/2018/5293568.
M. O. Onuorah and A. B. Namwanje, Neoline, “Optimal Control Model of Human African Trypanosomiasis,” World Sci. News, vol. 178, no. February, pp. 136–153, 2023.
G. Birkhoff, G., & Rota, “Ordinary differential equations,” john wiley& sons. Inc., 1978.
J. A. J. Diekmann, O., Heesterbeek, J. A. P., & Metz, “On the definition and the computation of the basic reproduction ratio r 0 in models for infectious diseases in heterogeneous populations,” J. Math. Biol., vol. 28, pp. 365–382., 1990.
P. Van Den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Math. Biosci., vol. 180, no. 1–2, pp. 29–48, 2002, doi: 10.1016/S0025-5564(02)00108-6.
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