Globalization has, among others, the effect of facilitating the rapid spread of an epidemic disease in all the regions of the earth.
In the last years, the dynamics of the spread of various kinds of epidemic diseases have been largely studied, in order to have a good model that can help to forecast the modalities of the geographic diffusion among nations with different social characteristics and healthy weakness, in view of prevention and therapeutic actions. These modalities depend on the dangerousness of the epidemic and/or on the general health of the population, on social habits and so on. When an epidemic affects one group in a region, it modifies the peculiarities of that group and therefore the corresponding epidemic model must be changed; in the meantime, the spread could start and involve subjects in other regions, thus resulting in a new global environmental and social situation.
In this project, the epidemic spread is faced considering a two-levels modeling; one level takes into account ¿in-regions¿ dynamics, whereas the other level considers ¿intra-regions¿ interactions. The awareness of the presence of a virus changes the interactions between the different elements of each region and, consequently, among all the regions, thus inducing a different scenario to be faced with suitable control strategies.
The main goals of this project are:
1. to propose a general mathematical description of a multilayer society epidemic spread over a geographical network;
2. to propose, in such a complex dynamical scenario, control strategies for optimal resource allocation, with and without the constraint of resource limitations;
3. to validate the approach referring to a study case, putting in evidence the effectiveness of the optimal control action.
As the references included confirm, the proposers of this project have experience in modeling and control the spread of different epidemics (SIR, influenza SIRC, HIV/AIDS).
The full development of this three-years project requires the fulfillment of several steps; the completion of each of them is an important result and all them contribute, also separately, to improvements both in the scientific and in the applicative contexts.
The main steps, described in the following, are represented by: data collection and analysis, models¿ development with identification and validation procedures, control design, in particular with optimal control techniques, first implementation on a case study, and analysis of possible extensions to different cases.
Data analysis: As usual for any real phenomenon, also the proposed modeling requires a preliminary suitable data collection and analysis; the available data are not homogeneous, for example social habits and customs, such as eating habits and general healthy conditions, and attitude of traveling; nevertheless, they influence the local (in-region) and global (intra-regions) spread of the epidemic. This means that the databases to be used contain a large amount of data probably larger than what is required and also in a non-homogeneous representation; the importance of the use of methodologies devoted to the collection, analysis and classification of big data sets is considerable during this phase. Data mining and machine learning techniques, as well as data analysis as the Principal Component one, will be adopted. Being this phase a time consuming one, the possibility to have the additional grant, requested in this project, can speed up the activities; also, the possibility of asking for external collaboration with experts of data analysis is considered.
The results of all this work will be a rich, homogeneous and well-classified database that can be adopted as a general set for the scientific community.
Models definitions: a mathematical model describing at the same time the interactions between classes of populations and geographically distributed populations is the main goal of this phase.
Based on the previous knowledge of the proposers and from the literature analysis, the initial idea is to adopt a multilayer network model; some preliminary examples are already available, but applied, up to now, to simple models of epidemic spreads, like the SIS one. A general description will be introduced, trying as much as possible not to refer to a specific disease, but focusing on the dynamics of the local and global interactions. The results obtained in this phase will represent an improvement in the modeling of small social dynamics contagious and geographically distributed epidemic spreads.
Control design: Several solutions are available for small scale epidemic spreads or for networked modeling of the interconnections. The models introduced represent rich and complex dynamics, requiring, consequently, a more sophisticated control design approach. Up to now, the introduction of optimal control actions in multilayer spread network has been done, for small systems, by means of numerical approach only, [11]; this is due to the dimensions of the problems and the complexity of the mathematical representations. The additional aim of this project is to introduce an optimal control scheme expressed in a mathematical closed form, proposing, whenever possible, constructive algorithms, as in [3]. The formal aspects of the closed form control design procedures and the methodologies developed, represent an important contribution in the control design theory.
Implementation: a realistic case study will be specifically addressed, from the analysis to the implementation of control actions. To help the operators to interact with the whole framework proposed, a user-friendly graphical interface will be designed, so improving the study of possible spreads of epidemic diseases and the simulation of different scenarios for prevention or fast intervention.
Clearly, such a graphical simulator is another possible contribution for the knowledge improvement.
Generalization: once the whole procedure will be evidenced for a selected case study, part of the project will be devoted to the analysis of possible generalization of the concepts, the methodologies and the results previously obtained. The possibility of applying the same approach slightly modified to different spreading processes on complex networks, like computer virus, or the spreading of rumors through social networks will be investigated.
The interdisciplinary of the research, involving mathematical modeling, data analysis, automatic control, social sciences and economics represent a strength of this project, allowing to yield a realistic description of epidemic spreads and to propose achievable control actions.
Despites many interesting works done on epidemic spread control, the last years epidemics as well as the more generalized spread of computer virus and/or news through different social networks, have shown some inadequacies in modeling and control, and the importance of managing these phenomena.