# Analytical Solution to the Mathematical Models of HIV/AIDS with Control in a Heterogeneous Population Using Homotopy Perturbation Method (HPM)

Analytical Solution to the Mathematical Models of HIV/AIDS with Control in a Heterogeneous Population Using Homotopy Perturbation Method (HPM)

David OmaleSaikat Gochhait

Mathematical Sciences Department, Kogi State University, Anyigba, India

Symbiosis Institute of Telecom Management, Symbiosis International: Deemed University, Pune, India

Corresponding Author Email:
davidubahi@gmail.com
Page:
20-34
|
DOI:
https://doi.org/10.18280/ama_a.550103
20 February 2018
| |
Accepted:
26 March 2018
| | Citation

OPEN ACCESS

Abstract:

A mathematical model for the control for HIV/AIDS was formulated, using vaccine, condom, therapeutic dose and public health campaign’; The models are compartmental in nature and non-linear. We use Homotopy perturbation method to solve the model. It was discovered that, any non-linear equation to be easily solved using this method, it is explicit and converge easily.

Keywords:

homotopy, perturbation, HIV/AIDS control, condom, therapeutic dose model

1. Introduction
2. Basic IDEA of He’S Homotopy Perturbation Method
3. Solution of the Models Using HPM
4. Conclusion
References

[1] He JH. (2003). Homotopy perturbation method for new nonlinear analytical technique. Applied Mathematics and Computation 135: 73-79.

[2] He JH. (2006). Homotopy perturbation method for solving boundary value problem. Physics Letters A 350: 87–88.

[3] Taghipour R. (2011). Application of Homtopy perturbation method on some linear and nonlinear parabolic equations IJRRAS 6(1): 55-59.

[4] Sepkowitz KA. (2001). AIDS the first 20 years. N. Engl J. Med. 344(23).

[5] WHO (World Health Organization (2007). WHO case definition of HIV for surveillance and revised clinical staging and immunological classification of HIV related disease in Adults and children. Geneval pp. 6-16.

[6] Vogel M, Schwarze-Zander C, Wasmuth JC, Spengler U, Sauerbruch T, Rockstroh JK. (2010). The treatment of patient with HIV. Deutsches Arzteblatt International 107(28-29).

[7] Evian C. (2006). Primary HIV/AIDS care: a practical guide for primary health care personal in a clinical and supportive setting. Houghton (South Africa): Jacana P. 29.

[8] Elliot T. (2012). Lecture Notes: Medical Microbiology and Infection. John Wiley and Sons. p. 273.

[9] Blankson JN. (2010). Control of HIV-1 replication in elite suppressors. Discovery Medicine 9(46).

[10] Walker BD. (2007). Elites control of HIV infection implication for vaccine and treatment. International AIDS Society USA 15(4).

[11] Holmes CB, Losina E, Walenskey RP. (2003). Review of human immunodeficiency virus type-1 related opportunistic infections in Sub-Sahara Africa clin. Infect Dis 36(5).

[12] Sestak K. (2005). Chronic diarrhea and AIDS insights into studies with non-human primate curr. HIV Res 3(3).

[13] Murray ED, Buttner N, Brice BH. (2012). Depression and psychosis in Neurological practice. Philadeplina PA Elsevien /Saunders p. 101.