Analysis and Control of a Dynamical Model for HIV Infection With One or Two Inputs

Analysis and Control of a Dynamical Model for HIV Infection With One or Two Inputs

Lazaros Moysis (Aristotle University of Thessaloniki, Greece), Ioannis Kafetzis (Aristotle University of Thessaloniki, Greece) and Marios Politis (General Hospital of Thessaloniki “G. Papanikolaou”, Greece)
Copyright: © 2018 |Pages: 25
DOI: 10.4018/978-1-5225-4077-9.ch012


A dynamical model that describes the interaction between the HIV virus and the human immune system is presented. This model is used to investigate the effect of antiretroviral therapy, consisting of RTI and PI drugs, along with the result of undesired treatment interruption. Furthermore, the effect of both drugs can be combined into a single parameter that further simplifies the model into a single input system. The value of the drug inputs can be adjusted so that the system has the desired equilibrium. Drug administration can also be adjusted by a feedback control law, which although it linearizes the system, may have issues in its implementation. Furthermore, the system is linearized around the equilibrium, leading to a system of linear differential equations of first order that can be integrated into courses of control systems engineering, linear and nonlinear systems in higher education.
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1. Introduction

The infection from the human immunodeficiency virus constitutes a global pandemic. According to the recent report of the Joint United Nations Programme on HIV/AIDS (UNAIDS, 2014), from its first occurrence until today, more than 78 million people have been infected with HIV and 39 million have died from causes related to HIV/AIDS. By the end of 2014, 36.99 million people were living with HIV, of which 3.2 million are children, 2.1 million are young adults and 4.2 million are over 50 years old. Around 70% of HIV positive persons live in regions of sub-Saharan Africa.

The number of people being infected with HIV is decreasing in most countries. In 2015 there was an accounting of 2.1 million new HIV infections, a number that is 38% lower than the 3.4 million infections reported in 2001. There is also a steady decrease in the number of deaths from AIDS. In 2013 for example, 1 million deaths from AIDS have been reported, which corresponds to a 35% decrease compared with 2005.

Results regarding antiretroviral therapy are positive and reflect the steps forward that have been taken in the last years. The number of persons with no access to therapy in 2006 was as high as 90%, while in 2013 they have been decreased to 63%. In 2015, the number of people with access to therapy was 15.8 million, while today they are about 17 million, which is 2 million higher than the aim that the United Nations had set for 2015.

An important part in the epidemiological analysis of HIV infection is the high risk groups. By that, we refer to population groups where the infection occurs with a higher frequency than that of the general population. These groups have a higher infection risk all around the globe. More specifically, men who have sex with men are 19 times more likely to be infected with HIV. Injecting drug users have 28 times higher likelihood than the general population. Around 12.7 million injecting drug users are reported worldwide, of which 13% are HIV positive. Another risk group is the one of sex industry workers, with 12 times higher likelihood than the general population. In addition, transgender women are 49 times more likely to live with the HIV virus than other adults of the same age.

Specifically, in Greece, according to the recent HIV/AIDS surveillance report on October of 2015 (H.C.D.C.P., 2015), the Hellenic Center For Disease Control & Prevention (H.C.D.C.P.) has so far reported 15.109 positive HIV infections. Of these, 3.782 have already developed AIDS and around 7.700 are subject to antiretroviral therapy (ART). The number of deaths resulting from the infection amounts to 2.562. According to the H.C.D.C.P. 2014 report (H.C.D.C.P., 2014), the largest portion of HIV cases has been diagnosed in men who had sex with men (46.2%), followed by the categories of heterosexual sexual contact (21.3%) and injecting drug users (10.8%).

More specifically, during the period of 2011-2013, there was a big rise in the number of cases regarding injecting drug users. This rise, that amounted in 2012 to 9.6 new infections per 100000 people is strongly contributed to the economic crisis in Greece, and is a testament to the key part that social (homelessness, imprisonment) and economic factors (austerity) play in the disease transmission in high risk groups (Hatzakis et al. 2015; Tsang et al. 2015). The role that Big Events, such as the economic crisis, play in the creation of hazardous environments that promote infectious diseases like HIV by causing economic instability, population displacement, inter-communal violence, drug consumption and youth alienation where investigated in (Nikolopoulos et al. 2015).

This HIV outbreak was followed by a steady decrease during the last two years (2014-2015) with around 6.2 infections per 100000 people. This was possibly the result of various prevention and awareness programs that were implemented, focusing on high risk groups (Nikolopoulos et al. 2016; Nikolopoulos & Fotiou, 2015; Sypsa et al. 2017). Yet, as the Office for HIV and Sexually Transmitted Diseases emphasizes, although the last data on the decrease infections are positive, they should not be considered comforting. There must be constant actions to raise the awareness of both the high risk groups and the general population.

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