The New Stochastic Differential Equations Model for Controlling the Spread of Viral Diseases: HIV as an Example
DOI:
https://doi.org/10.24237/Keywords:
HIV disease, Basic reproduction rate, Computer simulation, Disease-free point, Stochastic differential equations.Abstract
The main goal of presenting this manuscript is to study the dynamic activities of HIV spread and how to prevent it. The disease behavior was studied by proposing a new stochastic mathematical model. The solution's existence and uniqueness for the proposed mathematical model have been proven. We have also demonstrated the restrictions that must be met for society to rid itself of the scourge of the transmission of HIV by finding the basic reproduction rate. if the basic reproduction rate is less than one this means the disease-free point is stable. Conversely, if the basic reproduction rate is greater than one this means the disease - free point is unstable. The theoretical results were proven numerically through computer simulation using MATLAB.
Downloads
References
[1] World Health Organization,Jul 22, 2024 — HIV (human immunodeficiency virus) infects cells of the immune system. Infection.
[2] M. Sohaib, Mathematical Modeling and Numerical Simulation of HIV Infection
[3] S. N. Majeed, R. K. Naji, An Analysis of A partial Temporary Immunity SIR Epidemic Model with Nonlinear Treatment Rate, Baghdad Sci. J., 16(3), 639-647(2019), DOI(http://dx.doi.org/10.21123/bsj.2019.16.3.0639)
[4] S. Saravanakumar, A .Eswari, L. Rajendran, M. Abukhaled, A mathematical Model of Risk Factors in HIV/AIDS Transmission Dynamics: Observational Study of Female Sexual Network in India, Appl. Math. Inf. Sci., 14(6), 967-976(2020), DOI(http://dx.doi.org/10.18576/amis/140603)
[5] A. Raza, A. Ahmadian, M. Rafiq, S. Salahshour, M. Naveed, M. Ferrara, A. H .Soori, Modeling the Effect of Delay Strategy on Transmission Dynamics of HIV/AIDS Disease, Adv. Differ. Equ., 1 -13(2020), DOI(https://doi.org/10.1186/s13662-020-03116-8)
[6] S. W. Teklu, B. S. Kotola, A dynamical Analysis and Numerical Simulation of COVID-19 and HIV/AIDS Co-infection with Intervention Strategies, J. Biol. Dyn., 17(1), 2175920(2023),DOI(https://doi.org/10.1080/17513758.2023.2175920)
[7] J. Zhang, X. Ma, Z. Jin, Stability Analysis of an HIV/AIDS Epidemic Model with Sexual Transmission in A patchy Environment, J. Biol. Dyn., 17(1), 2227216(2023), DOI(https://doi.org/10.1080/17513758.2023.2227216)
[8] S. W. Teklu, T. T. Mekonnen, HIV/AIDS‐Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation, J. Appl. Math., 2021(1), 5444605(2021), DOI(https://doi.org/10.1155/2021/5444605)
[9] A.J.Arenas, G.González-Parra, J.J. Naranjo, M. Cogollo, N.De La Espriella, Mathematical Analysis and Numerical Solution of A model of HIV with A discrete Time Delay, Mathematics, 9(3), 257(2021), DOI(https://doi.org/10.3390/math9030257)
[10] R.Wattanasirikosone, C. Modnak, Analysing Transmission Dynamics of HIV/AIDS with Optimal Control Strategy and Its Controlled State, J. Biol. Dyn., 16(1), 499-527(2022), DOI(https://doi.org/10.1080/17513758.2022.2096934)
[11] S. W. Teklu, K. P. Rao, HIV/AIDS‐Pneumonia Codynamics Model Analysis with Vaccination and Treatment, Comput. Math. Methods Med, 2022(1), 3105734(2022), DOI(https://doi.org/10.1155/2022/3105734)
[12] B. Seidu, O. D .Makinde, C. S. Bornaa, Mathematical Analysis of an Industrial HIV/AIDS Model that Incorporates Carefree Attitude towards Sex, Acta biotheoretica, 69(3), 257-276(2021), DOI(https://doi.org/10.1007/s10441-020-09407-7)
[13] A. M. Kareem, S. N. Al-Azzawi, A stochastic differential equations model for the spread of coronavirus COVID-19): the case of Iraq, Iraqi Journal of Science, 62(3),
1025-1035(2021), DOI(https://doi.org/10.24996/ijs.2021.62.3.31)
[14] D. Wanduku, On The Almost Sure Convergence of A stochastic Process in A class of Nonlinear Multi-Population Behavioral Models for HIV/AIDS with Delayed ART Treatment, Stochastic Analysis and Applications, 39(5), 861-897(2021), DOI(https://doi.org/10.1080/07362994.2020.1848593)
[15] A. M. Kareem, S. N. Al-Azzawi, Comparison Between Deterministic and Stochastic
Model for Interaction (COVID-19) With Host Cells in Humans, Baghdad Science
Journal, 19(5), 1140-1147(2022), DOI(http://dx.doi.org/10.21123/bsj.2022.6111)
[16] A. Tesfay, T. Saeed, A. Zeb, D. Tesfay, A. Khalaf, J. Brannan, Dynamics of A stochastic COVID- 19 Epidemic Model with Jump-Diffusion, Adv. Differ. Equ, 2021(1), 228(2021), DOI(https://doi.org/10.1186/s13662-021-03396-8)
[17] A. M. Kareem, S. N. Al-Azzawi, A stochastic Differential Equations Model for Internal COVID-19 Dynamics, J. Phys. Conf. 2021, 1818(1), 012121(2021), DOI(http://dx.doi.org/10.1088/1742-6596/1818/1/012121)
[18] X. Wang,Y. Tan, Y .Cai, K.Wang, W. Wang, Dynamics of A stochastic HBV Infection Model with Cell-to-Cell Transmission and Immune Response, Math. Biosci. Eng, 18, 616-642(2021), DOI(https://doi.org/10.3934/mbe.2021034)
[19] D. Lestari, F. Adi-Kusumo, N. Y. Megawati, N. Susyanto, A minimum Principle for Stochastic Control of Hepatitis C Epidemic Model, Bound. Value Probl, 52(1), (2023), DOI(https://doi.org/10.1186/s13661-023-01740-3)
[20] A. M. Kareem, Stochastic differential equations model for the prevalence of illicit drug abuse and infectious diseases, In: AIP Conference Proceedings, 3264(1), (2025), DOI(https://doi.org/10.1063/5.0258458)
[21] A. Khan,G. Hussain, M. Zahri, G. Zaman, U. Wannasingha Humphries, stochastic SACR Epidemic Model for HBV Transmission, J. Biol. Dyn., 14(1), 788-801(2020), DOI(https://doi.org/10.1080/17513758.2020.1833993)
[22] A. M. Kareem ,F. J. Wafar, Stochastic differential equations model for the interaction of HCV with liver cells, Academic Science Journal, 2(4), 241-257(2024), DOI(https://doi.org/10.24237/ASJ.02.04.794B)
Downloads
Published
Issue
Section
License
Copyright (c) 2025 CC BY 4.0
This work is licensed under a Creative Commons Attribution 4.0 International License.
