Estimating Upsurge of Hiv Cases in Malaysia by Using Heun's Predictor-Corrector Method

Authors

  • Sabastine Emmanuel School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
  • Saratha Sathasivam School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
  • Nur Haziqah Izni Hasmadi School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
  • Nur Hakimah Mohamad Nasir School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
  • Muraly Velavan School of General and Foundation Studies, AIMST University, 08100 Bedong, Kedah, Malaysia

DOI:

https://doi.org/10.37134/jsml.vol12.1.6.2024

Keywords:

HIV, Transmission, Epidemic, Heun's method, Dynamics, Trends

Abstract

The prevalence of HIV/AIDS remains a significant global health concern, including in Malaysia. In this study, a mathematical model was developed to simulate the dynamics of HIV transmission and progression within the Malaysian population. The model incorporates various factors such as population size, infection rate, progression to AIDS, recruitment, natural death, and death due to the disease. Heun's predictor-corrector method was applied to numerically solve the model equations and predict the population of susceptible individuals, infected individuals, and AIDS cases over time. Real-world data on HIV/AIDS cases in Malaysia were used to validate the model and provide accurate predictions. The results indicated a gradual decline in the number of susceptible individuals and an increase in the number of infected individuals and AIDS cases over the simulation period. These findings can contribute to a better understanding of the dynamics of HIV/AIDS transmission in Malaysia and aid in the development of effective prevention and control strategies. Further research and refinement of the model are essential for continuous monitoring and projection of the HIV/AIDS epidemic in Malaysia, facilitating timely interventions and resource allocation for healthcare planning and policy-making.

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Author Biography

Sabastine Emmanuel, School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Department of Mathematics, Faculty of Science, Federal University Lokoja, 260102 Lokoja, Kogi, Nigeria

References

Abdallah SW, Estomih SM, Oluwole DM. (2012). Mathematical modelling of HIV/AIDS dynamics with treatment and vertical transmission. Applied Mathematics, 2(3), 77-89.

Agarwala BD (2002). On two ODE models for HIV/AIDS development in Canada and a logistic SEIR model. Far East Journal of Applied Mathematics, 6(1), 25-70.

Anderson RM, May RM, Johnson. (1998). A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. Mathematical Medicine and Biology: A Journal of the IMA, 3, 229-263.3.

Barre SF, Chermann JC, Rey F, Nugeyre MT, Chamaret S, Gruest J, Montagnier L. (1983). Isolation of a T-lymphotropic retrovirus from a patient at risk for acquired immune deficiency syndrome. AIDS Science, 220(4599), 868-871.

Barsotti S, Neri A, Scire JS. (2008). The VOL‐CALPUFF model for atmospheric ash dispersal: 1. Approach and physical formulation. Journal of Geophysical Research: Solid Earth, 113(3), 1-12.

Busenberg S, Cooke K. (1995). Vertically transmitted diseases models and dynamics. Springer Berlin, Heidelberg.

Carlos CC, Zhilan F, Wenzhang H. (2001). On the computation of RO and its role on global stability. In: Castillo-Chavez PC, Blower S, Driessche P, Kirschner D, Yakubu AA. Eds., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer, Berlin.

Cassels S, Clark SJ, Morris M. (2008). Mathematical models for HIV transmission dynamics: tools for social and behavioral science research. Journal of Acquired Immune Deficiency Syndromes, 47(1), 34-39.

Coovadia H. (2004). Antiretroviral agents-how best to protect infants from HIV and save their mothers from AIDS. The New England Journal of Medicine, 351(3), 289-292.

Eshetu DG, Boka KB, Purnachandra RK. (2020). Mathematical Modelling of HIV/AIDS transmission dynamics with drug resistance compartment. American Journal of Applied Mathematics, 8(1), 34-45.

Emmanuel S, Sathasivam S, Ali MKM, Kee TJ, Ling YS. (2023). Estimating the transmission dynamics of Dengue fever in subtropical Malaysia using SEIR model. Journal of Quality Measurement and Analysis, 19(2), 45-56.

Lopez‐Gonzalez MDLL, Quemada‐Villagomez ML, Martinez‐González GM, Oliveros‐Munoz JM, Jimenez‐Islas H. (2023). A novel predictive homotopic path tracking algorithm to solve non‐linear algebraic equations. The Canadian Journal of Chemical Engineering, 101(6), 3382-3408.

Maimunah DA. (2018). A mathematical model for HIV spreads control program with ART treatment. Journal of Physics: Conference Series, 974, 012035.

Mother-to-child HIV transmission in Africa. Policy Fact. AVERT (2010), HIV treatment. http://www.avert.org/treatment.html. Retrieved on 24th December 2010.

Mukandavire Z, Mitchell KM, Vickerman P. (2016). Comparing the impact of increasing condom use or HIV pre-exposure prophylaxis (PrEP) use among female sex workers. Epidemics, 14, 62-70.

Stilianakis NI, Dietz K, Schenzle D. (1997). Analysis of a model for the pathogenesis of AIDS. Mathematical Biosciences, 145(1), 27-46.

Timothy LM, Daniel T, Halperin. (2008). Concurrent sexual partnerships and the HIV epidemics in Africa: evidence to move forward. AIDS Behaviour, 14, 11-16.

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Published

2024-01-05

How to Cite

Emmanuel, S., Sathasivam, S., Hasmadi, N. H. I., Mohamad Nasir, N. H., & Velavan, M. (2024). Estimating Upsurge of Hiv Cases in Malaysia by Using Heun’s Predictor-Corrector Method. Journal of Science and Mathematics Letters, 12(1), 43–52. https://doi.org/10.37134/jsml.vol12.1.6.2024

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