### Mathematical modelling of the dynamics of AIDS epidemics development in the world

#### Abstract

In this work, mathematical modelling of the dynamics of AIDS epidemics development in the world is performed for the following countries: Russian Federation, Austria, France and Brazil. HIV infection and AIDS are the diseases for which the development is under special control of international community. Annual HIV infection morbidity is up to 3 million cases a year, and the average age of the infected varies over the range of 20-30 years. At the moment, there is no cure for HIV infection. Without supporting treatment, it leads to the development of acquired immune deficiency syndrome (AIDS) and death. Consequently, the spreading of HIV leads to serious economic loss. Mathematical methods are widely applied to the analysis of HIV spreading, forecasting the epidemic development and qualitative evaluation of measure effectiveness. Mathematical description of the HIV epidemic development process allows analyzing the character of the disease for each region deeper, perform the comparative study of statistical and modelled data, make suggestions on further possibilities of HIV infection development and confirm the importance of introducing federal measures of confronting human immunodeficiency viruses. Therefore, authors provide the results of analyzing statistical data for the counties mentioned above, mathematical models of AIDS epidemic development and results of modelling for each region. Over the course of this work, optimal parameter values have been found for an accurate description of statistical data. A comparative study of the current situation for AIDS epidemic in Russian Federation, Austria, France and Brazil. As a result, the conclusion of effectiveness of present measures of confronting HIV infection in these countries.

#### Full Text:

PDF#### References

Hertog S. and Sawyer C. Mortality and the HIV/AIDS Epidemic. 2015; 834-843. DOI: 10.1016/B978-0-08-097086-8.31051-0

Haacker M. HIV/AIDS, Macroeconomic Effect of. 2014; 462-467. DOI: 10.1016/B978-0-12-375678-7.00610-6

Brauer F. Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling. 2017; 2.2: 113-127. DOI: 10.1016/j.idm.2017.02.001

Hyman J. M., Stanley E. A. Using mathematical models to understand the AIDS epidemic. Mathematical Biosciences. 1988; 90.1-2: 415-473. DOI: 10.1016/0895-7177(89)90252-5

Hernandez-Vargas E. A., Middleton R. H. Modeling the three stages in HIV infection. Journal of theoretical biology. 2013; 320: 33-40. DOI: 10.1016/j.jtbi.2012.11.028

Biswas M. H. A. AIDS epidemic worldwide and the millennium development strategies: A light for lives. HIV and AIDS Review. 2012; 11.4: 87-94. DOI: 10.1016/j.hivar.2012.08.004

Huo H. F., Chen R., Wang X. Y. Modelling and stability of HIV/AIDS epidemic model with treatment. Applied Mathematical Modelling. 2016; 40.13-14: 6550-6559. DOI: 10.1016/j.apm.2016.01.054

Getz W. M., Salter R., Muellerklein O., Yoon H. S., Tallam K. Modeling epidemics: A primer and Numerus Model Builder implementation. Epidemics. 2018. DOI: 10.1016/j.epidem.2018.06.001

Dutta A. and P. K. Gupta. A mathematical model for transmission dynamics of HIV/AIDS with effect of weak CD4+ T cells. Chinese journal of physics. 2018; 56.3: 1045-1056. DOI: 10.1016/j.cjph.2018.04.004

Khan A. et al. Stability analysis and numerical solutions of fractional order HIV/AIDS model. Chaos, Solitons & Fractals. 2019; 122: 119-128. DOI: 10.1016/j.chaos.2019.03.022

Denisov B. P., Sakevich V. I. The dinamics of HIV/AIDS epidemic. Socialnie issledovaniya. 2004, (1): 75-85. Available at: https://elibrary.ru/item.asp?id=17670471 (accessed 20.01.2019). (In Russian)

Denisov B. P., Sakevich V. I. Forecast of possible demographic consequences of HIV/AIDS epidemic in the Russian Federation. Problemy Prognozirovaniya. 2005, 3: 149-160. Available at: https://elibrary.ru/item.asp?id=9128494 (accessed 20.01.2019). (In Russian)

Nosova E.A. Models of control and spread of HIV-infection. Mathematical biology and bioinformatics. 2012; 7.2: 632-675. DOI: 10.17537/2012.7.632

W. O. Kermack, and A. G. McKendrick. Contributions to the mathematical theory of epidemics. Proceedings of the Royal Society of Edinburgh, Section A. Mathematics. 1927, 115:700–721. DOI: 10.1098/rspa.1927.0118

Huang X. C., Villasana M. An extension of the Kermack–McKendrick model for AIDS epidemic. Journal of the Franklin Institute. 2005; 342.4: 341-351. 10.1016/j.jfranklin.2004.11.008

Khaleque A. and Sen P. An empirical analysis of the Ebola outbreak in West Africa. Scientific reports. 2017, 7: 42594. DOI: 10.1038/srep42594

Urakova K. A., Khrapov P. V., Mathematical modelling of Ebola hemorrhagic fever epidemiological development in West Africa. Almanakh sovremennoi nauki I obrazovaniya. 2017, 4-5 (118):97-99. Available at: https://elibrary.ru/item.asp?id=29147514 (accessed 10.01.2019). (In Russian)

Khrapov N. P., Khrapov P. V., Shumilina A. O. Mathematical Model and forecast of AIDS epidemiological development. Almanakh sovremennoi nauki I obrazovaniya, Gramota. 2008, 12(9):218-221. Available at: http://scjournal.ru/articles/issn_1993-5552_2008_12_70.pdf. (In Russian)

Holt E. Disputed figures do not hide Russia's HIV epidemic. The Lancet HIV. 2019; 6.4: 216-217. DOI: 10.1016/S2352-3018(19)30085-2

Suryapranata F., Boyd A., Grobusch M. P., Prins M., Sonder G.

Symptoms of infectious diseases in HIV-positive travellers: A prospective study with exposure-matched controls. Travel medicine and infectious disease. 2019. DOI: 10.1016/j.tmaid.2019.01.003

Dinh L., Chowell G., Rothenberg R. Growth scaling for the early dynamics of HIV/AIDS epidemics in Brazil and the influence of socio-demographic factors. Journal of theoretical biology. 2018; 442: 79-86. DOI: 10.1016/j.jtbi.2017.12.030

Etienne L., Delaporte E., Peeters M. Origin and Emergence of HIV/AIDS. Genetics and Evolution of Infectious Disease (Second Edition). 2017, 573-599. DOI: 10.1016/B978-0-12-799942-5.00025-1

Martcheva M. An Introduction to Mathematical Epidemiology. Springer. 2015, 453 p. DOI: 10.1007/978-1-4899-7612-3

Woodyatt C. R. World AIDS Day 2018. 2018, 8(12):829-829. DOI: 10.1016/j.annepidem.2018.10.009

Põder A., Haldre M. HIV in Europe. Clinics in dermatology. 2014, 32.2: 282-285. DOI:10.1016/j.clindermatol.2013.08.011.

### Refbacks

- There are currently no refbacks.

Abava Absolutech IT-EDU 2019

ISSN: 2307-8162