In this project the problem of HIV/AIDS diffusion is faced ; a new model recently proposed is considered. It assumes two classes of susceptible subjects: the ones with wise behaviours and the one that by incautious acts could contract the virus. The infected subjects are divided into three classes: the ones not aware of their status (and therefore could infect other subjects), the patients in the pre-aids status and the aids patients. The HIV/AIDS spread has two main particularities . The first one is that with wise behavior its diffusion could be drastically reduced. The second particularity is that there is a period, more or less long (up to 10 years), in which the symptoms of the disease are not evident; therefore, among infected subjects the most dangerous are those (up to 54% of the entire infected population) that, not aware of their status, could infect the unwise susceptible subjects. Currently no vaccine exists and the treatment consists in standard antiretroviral therapy . This model allows to propose suitable control actions according to the indications of the World Health Organization: 1) a control designed for healthy people (information campaign); 2) a control devoted to a fast identification of new infections (test campaign); 3) medication to the aware infected subjects.
The costs of prevention 1 and 2 represent an immediate economic effort, whereas their effects could be noted only in the future. Therefore, a schedule of the control action is advisable. This project aims at determining the optimal resources allocation both in presence of full information and in the realistic case when only partial data are available. The introduction of control actions could be performed taking into account the problem of resource limitations, both from the economic point of view and the logistic one. It could be faced, introducing a suitable cost index. The problem of not complete information could be addressed by using an observator.
The novelties of this project involve different levels and may be listed in the following items:
- Modeling: The considered model [Di Giamberardino et al 2017] appears to be a good compromise in order to describe the modalities of HIV/AIDS transmission. Nevertheless the delay occurring among the infection and the awareness of the illness are rather significant (up to 10-15 years) and probably it could be included in the model. Moreover the new migration flows could be studied and eventually introduced in the model. In the considered model it is assumed that new incomers are not infected; now a complete model could assume that they could belong to any of the possible categories. Social behaviors will be taken into account by studying specific communities and ages and integrating, if necessary, the considered model.
At the best of our knowledge what is usually studied when dealing with HIV/AIDS spread is a population in which there are the susceptible and three classes of infected., whereas in the present approach a more accurate description of the susceptible is assumed and represents the basis for a further improvement, for example referring to specific categories of people or to specific ages.
- Model analysis: A deep analytical analysis of the model; it is a nonlinear model and up to now its stability has been studied by means of a linearization in the neighborhood of the equilibria points . An accurate analysis could include the determination, if it exists, of a bifurcation point and the direct study of the nonlinear system, without any approximation
- Model identification: in the considered model some of the parameters have been taken from literature and some of them have been chosen in a wise way. Nevertheless, by using real data available from the World Health Organization website or, more specifically for Italy, from the website of the Istituto Superiore di sanità, an identification of the model could be determined thus aiming at a reliable description of the HIV/AIDS spread.
The identification of the model that adequately describe the HIV/AIDS spread could represent a tool to test the effectiveness of prevention campaigns and suggest eventually different strategies and scheduling.
- Control actions: The introduction of control actions could be performed taking into account the problem of resource limitations, both from the economic point of view and the logistic one. A problem of optimal resource allocation could be faced, introducing a suitable cost index.
- Control actions: In the realistic case the only assessed information is about the infected subjects, the HIV/AIDS patients. All the modeled categories are not available, since all the subjects not tested could be healthy or infected. The problem of not complete information could be addressed by using an observator. Due to the nonlinearity of the system, different choices could be tested in order to determine a reliable estimation of the state.
In literature, the control is generally devoted to induce infected subjects to the Long Term Non Progressor Status (LTNP): it is the status of the HIV patients who still have enough CD4 T-cells to contrast HIV and other infections and never develop AIDS; they represent less than 1% of the HIV infected patients. The aim is to drive, with medication, the state of the patient into the LNTP region of attraction.
In the present project the intervention actions are considered together aiming both at prevention and at medication, by using in an optimal way, the available bounded resources.
- Interdisciplinarity: the model considered and the optimal resource allocation solution could be used in different scenarios, where interactions among mutual-exclusive categories are present.
P.Di Giamberardino, L. Compagnucci, C.De Giorgi, D.Iacoviello, A new model of the HIV/AID infection diffusion and analysis of the intervention effects, IEEE -MED Conference 2017
H. Shim, N. H. Jo, H. Chang and J. H. Seo, ¿A system theoretic study on a treatment of AIDS patient by achieving long
term non-progressor¿, Automatica, 45(3), pp. 611¿612, 2009