Optimal control analysis for modeling HIV transmission

Document Type : Research Article

Author

Department of Mathematics, Wollega University, Nekemte, Ethiopia.

Abstract

In this study, a modified model of HIV with therapeutic and preventive controls is developed. Moreover, a simple evaluation of the optimal control problem is investigated. We construct the Hamiltonian function by way of integrating Pontryagin’s maximal principle to achieve the point-wise optimal solution. The effects obtained from the version analysis strengthen public health education to a conscious population, PrEP for early activation of HIV infection prevention, and early treatment with artwork for safe life after HIV infection. Moreover, numerical simulations are done using the MATLAB platform to illustrate the qualitative conduct of the HIV infection. In the end, we receive that adhering to ART protective prone people, the usage of PrEP along with different prevention control is safer control measures.

Keywords

Main Subjects


[1] Ali Biswas, H. On the evolution of AIDS/HIV treatment: an optimal control approach, Curr. HIV Res. 12(1), (2014), 1–12.
[2] Akudibillah G., Pandey A., and Medlock J. Optimal control for HIV treatment. Math. Biosci. Eng. 16(1), (2018), 373–396.
[3] Arenas, A.J., González-Parra, G., Naranjo, J.J., Cogollo, M. and De La Espriella, N. Mathematical analysis and numerical solution of a model of HIV with a discrete time delay, Mathematics, 9(3), (2021), 257.
[4] Bakare, E.A. and oskova-Mayerova S.Optimal control analysis of cholera dynamics in the presence of asymptotic transmission, Axioms 10 (2), (2021), 60.
[5] Bórquez, A., Guanira, J.V., Revill, P., Caballero, P., Silva-Santisteban, A., Kelly, S., Salazar, X., Bracamonte, P., Minaya, P., Hallett, T.B. and Cáceres, C.F. The impact and cost-effectiveness of combined HIV prevention scenarios among transgender women sex-workers in Lima, Peru: a mathematical modelling study, The Lancet Public Health, 4(3), (2019), e127–e136.
[6] Boukhouima, A., Lotfi, E.M., Mahrouf, M., Rosa, S., Torres, D.F. and Yousfi, N. Stability analysis and optimal control of a fractional HIV-AIDS epidemic model with memory and general incidence rate, Eur. Phys. J. Plus, 136(1), (2021), 1–20.
[7] Camlin, C.S., Koss, C.A., Getahun, M., Owino, L., Itiakorit, H., Akatuk-wasa, C., Maeri, I., Bakanoma, R., Onyango, A., Atwine, F. and Ayieko, J. Understanding demand for PrEP and early experiences of PrEP use among young adults in rural Kenya and Uganda: a qualitative study, AIDS Behav. 24, (2020), 2149–2162.
[8] Campos, C., Silva, C.J. and Torres, D.F. Numerical optimal control of HIV transmission in Octave/MATLAB, Math. Comput. Appl. 25(1) (2020), Paper No. 1, 20 pp.
[9] Campos, N.G., Lince-Deroche, N., Chibwesha, C.J., Firnhaber, C., Smith, J.S., Michelow, P., Meyer-Rath, G., Jamieson, L., Jordaan, S., Sharma, M. and Regan, C. Cost-effectiveness of cervical cancer screen-ing in women living with HIV in South Africa: a mathematical modeling study. Acquir. Immune Defic. Syndr. (1999), 79(2) (2018), 195.
[10] Cheneke, K.R. Optimal Control and Bifurcation Analysis of HIV Model, Comput. Math. Methods Med. (2023).
[11] Cheneke, K.R., Rao, K.P. and Edessa, G.K. Application of a new gen-eralized fractional derivative and rank of control measures on cholera transmission dynamics, International Journal of Mathematics and Math-ematical Sciences, 2021, (2021), 1–9.
[12] Cheneke, K.R., Rao, K.P. and Edessa, G.K. Bifurcation and stabillity analysis of HIV transmission model with optimal control, J. Math. 2021, (2021), 1–14.
[13] Choi, H., Suh, J., Lee, W., Kim, J.H., Kim, J.H., Seong, H., Ahn, J.Y., Jeong, S.J., Ku, N.S., Park, Y.S. and Yeom, J.S. Cost-effectiveness analysis of pre-exposure prophylaxis for the prevention of HIV in men who have sex with men in South Korea: a mathematical modelling study, Sci. Rep. 10(1), (2020), 14609.
[14] Ðorđević, J. and Rognlien Dahl, K., 2022. Stochastic optimal control of pre-exposure prophylaxis for HIV infection, Math, Med. Biol. 39(3), (2022), 197–225.
[15] Ghosh, I., Tiwari, P.K., Samanta, S., Elmojtaba, I.M., Al-Salti, N. and Chattopadhyay, J. A simple SI-type model for HIV/AIDS with media and self-imposed psychological fear, Math. Biosci. 306 (2018), 160–169.
[16] Hattaf, K. and Yousfi, N. Two optimal treatments of HIV infection model, World J. Model. Simul. 8(1), (2012), 27–36.
[17] Hattaf, K. and Yousfi, N. Optimal control of a delayed HIV infection model with immune response using an efficient numerical method, Int. Sch. Res. Notices, (2012).
[18] Hidayat, N., R. B. E. Wibowo, et al., Marsudi, Hidayat, N. and Wibowo, R. B. E. Optimal control and cost-effectiveness analysis of HIV model with educational campaigns and therapy, Matematika (Johor) 35 (2019), Special issue, 123–138.
[19] Hove-Musekwa, S.D., Nyabadza, F., Mambili-Mamboundou, H., Chiyaka, C. and Mukandavire, Z. Cost-effectiveness analysis of hospital-ization and home-based care strategies for people living with HIV/AIDS: the case of Zimbabwe, Int. Sch. Res. Notices, (2014).
[20] Huo, H.-F., Chen, R. and Wang, X.-Y. Modelling and stability of HIV/AIDS epidemic model with treatment, Appl. Math. Model. 40(13-14) (2016), 6550–6559.
[21] Huo, H.-F. and Li-Xiang, F. Global stability for an HIV/AIDS epidemic model with different latent stages and treatment. Applied Mathematical Modelling, 37(3) (2013), 1480–1489.
[22] Khajanchi, S., Bera, S. and Roy, T.K. Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes, Math. Comput. Simul. 180 (2021), 354–378.
[23] Marsudi, M., Hidayat, N. and Wibowo, R.B.E. Application of Optimal Control Strategies for the Spread of HIV in a Population, J. Life Sci. Res. 4(1) (2017), 1–9.
[24] Marsudi, T., Suryanto, A. and Darti, I. Global stability and optimal control of an HIV/AIDS epidemic model with behavioral change and treatment. Eng. Lett. 29(2) (2021).
[25] Naik, P.A., Yavuz, M., Qureshi, S., Zu, J. and Townley, S. Modeling and analysis of COVID-19 epidemics with treatment in fractional derivatives using real data from Pakistan, Eur. Phys. J. Plus, 135 (2020), 1–42.
[26] Olaniyi, S., Obabiyi, O.S., Okosun, K.O., Oladipo, A.T. and Ade-wale, S.O. Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics, Eur. Phys. J. Plus, 135(11) (2020), 938.
[27] Silva, C.J. and Torres, D.F. Modeling and optimal control of HIV/AIDS prevention through PrEP. arXiv preprint arXiv:1703.06446 (2017).
CAPTCHA Image