A comparative study between two systems with and without awareness in controlling HIV/AIDS

• Autorzy: Saha S. , Roy P. K.

Identyfikatory

DOI

10.1515/amcs-2017-0024

• Języki publikacji: EN

Abstrakty

EN

It has always been a priority for all nations to reduce new HIV infections by implementing a comprehensive HIV prevention programme at a sufficient scale. Recently, the ‘HIV counselling & testing’ (HCT) campaign is gaining public attention, where HIV patients are identified through screening and immediately sent under a course of antiretroviral treatment (ART), neglecting the time extent they have been infected. In this article, we study a nonlinear mathematical model for the transmission dynamics of HIV/AIDS system receiving drug treatment along with effective awareness programs through media. Here, we consider two different circumstances: when treatment is only effective and when both treatment and awareness are included. The model is analyzed qualitatively using the stability theory of differential equations. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed. These studies show that the aware populations were less vulnerable to HIV infection than the unaware population.

Słowa kluczowe

EN

epidemic model; HIV infection; awareness; antiretroviral therapy; basic reproductive number; numerical simulation

PL

model epidemiczny; zakażenie HIV; świadomość problemu; terapia antyretrowirusowa; podstawowy współczynnik reprodukcji; symulacja komputerowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 2
• Strony: 337--350
• Opis fizyczny: Bibliogr. 26 poz., rys., tab., wykr.

Twórcy

autor

Saha S.

• Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India

autor

Roy P. K.

• Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India

Bibliografia

• [1] Abiodun, G.J., Marcus, N., Okosun, K.O. and Witbooi, P.J. (2013). A model for control of HIV/AIDS with parental care, International Journal of Biomathematics 6(02): 1350006.
• [2] Al-arydah, M. and Smith, R. (2015). Adding education to test and treat: Can we overcome drug resistance?, Journal of Applied Mathematics 2015, Article ID 781270, DOI: 10.1155/2015/781270.
• [3] Barbalat, I. (1959). Syst`emes d’´equations diff`erentielles d’oscillations non-linéaires, Revue Roumaine de Mathématiques Pures et Appliquées 4(2): 267–270.
• [4] Bhunu, C., Garira, W. and Magombedze, G. (2009). Mathematical analysis of a two strain HIV/AIDS model with antiretroviral treatment, Acta Biotheoretica 57(3): 361–381.
• [5] Cai, L., Li, X., Ghosh, M. and Guo, B. (2009). Stability analysis of an HIV/AIDS epidemic model with treatment, Journal of Computational and Applied Mathematics 229(1): 313–323.
• [6] Castillo-Chavez, C., Blower, S., Driessche, P., Kirschner, D. and Yakubu, A.-A. (2002). Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory, Springer, New York, NY.
• [7] Castillo-Chavez, C. and Song, B. (2004). Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering 1(2): 361–404.
• [8] Chatterjee, A.N. and Roy, P.K. (2012). Anti-viral drug treatment along with immune activator IL-2: A control-based mathematical approach for HIV infection, International Journal of Control 85(2): 220–237.
• [9] Chatterjee, A.N., Saha, S. and Roy, P.K. (2015). Human immunodeficiency virus/acquired immune deficiency syndrome: Using drug from mathematical perceptive, World Journal of Virology 4(4): 356.
• [10] Elbasha, E.H. and Gumel, A.B. (2006). Theoretical assessment of public health impact of imperfect prophylactic HIV-1 vaccines with therapeutic benefits, Bulletin of Mathematical Biology 68(3): 577.
• [11] Gumel, A.B., Castillo-Chavez, C.,Mickens, R.E. and Clemence, D.P. (2006). Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges, Vol. 410, American Mathematical Society, Boston, MA.
• [12] Hove-Musekwa, S.D. and Nyababza, F. (2009). The dynamics of an HIV/AIDS model with screened disease carriers, Computational and Mathematical Methods in Medicine 10(4): 287–305.
• [13] Hyman, J.M., Li, J. and Stanley, E.A. (2003). Modeling the impact of random screening and contact tracing in reducing the spread of HIV, Mathematical Biosciences 181(1): 17–54.
• [14] Kiss, I.Z., Cassell, J., Recker, M. and Simon, P.L. (2010). The impact of information transmission on epidemic outbreaks, Mathematical Biosciences 225(1): 1–10.
• [15] Korobeinikov, A. and Maini, P.K. (2004). A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Mathematical Biosciences and Engineering 1(1): 57–60.
• [16] Misra, A., Sharma, A. and Singh, V. (2011). Effect of awareness programs in controlling the prevalence of an epidemic with time delay, Journal of Biological Systems 19(02): 389–402.
• [17] Nyabadza, F. (2006). A mathematical model for combating HIV/AIDS in southern Africa: Will multiple strategies work?, Journal of Biological Systems 14(03): 357–372.
• [18] Roy, P.K. (2015). Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission, Springer, Singapore.
• [19] Roy, P. K., Saha, S. and Al Basir, F. (2015). Effect of awareness programs in controlling the disease HIV/AIDS: An optimal control theoretic approach, Advances in Difference Equations 2015(1): 217–234.
• [20] Samanta, S. and Chattopadhyay, J. (2014). Effect of awareness program in disease outbreak—a slow—fast dynamics, Applied Mathematics and Computation 237(8): 98–109.
• [21] Smith, R.J., Okano, J.T., Kahn, J.S., Bodine, E.N. and Blower, S. (2010). Evolutionary dynamics of complex networks of HIV drug-resistant strains: The case of San Francisco, Science 327(5966): 697–701.
• [22] Statistics (2006). Statistics of South Africa. Website of the mid-year population estimates, Statistical release P0302, South Africa, http://www.statssa.gov.za/publications.
• [23] Tripathi, A., Naresh, R. and Sharma, D. (2007). Modeling the effect of screening of unaware infectives on the spread of HIV infection, Applied Mathematics and Computation 184(2): 1053–1068.
• [24] UDAIDS/WHO (2014). Website of the UDAIDS/WHO epidemiological fact sheets on HIV and AIDS, http://www.who.int/hiv/en/.
• [25] UDAIDS/WHO (2015). Website of the UDAIDS/WHO epidemiological fact sheets on HIV and AIDS, http://www.who.int/hiv/en/.
• [26] Van den Driessche, P. and Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences 180(1): 29–48.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).