The research proposed aims to develop large scale dynamical models for viruses spread, including the modelling of climate effects. The dependency of viruses¿ diffusions from climate characteristics is a well-established fact. Models of epidemics spreads which include this effect usually works on prefixed scenarios or making use of recent acquired data. The result is that in both cases, the dynamics of the climate changes is not considered, working at steady state for supposed situations.
The point of view assumed in this project is the definition of a unique integrated mathematical model which considers both the epidemics aspects and the climate ones, being able to produce simulated effects also during the changing of climate characteristics, independently from the fact that these changes are fast or slow, under real or supposed conditions. Moreover, the continuous spatial representation of the epidemic spreads allows to work with geographical maps of diseases diffusion.
This idea to integrate in an effective way the climate evolution to the epidemics diffusion is supported by the fact that they both are strongly related to the environment over which they evolve. In fact, the orography, the temperature, the presence of water surfaces, the oceanic currents, the presence of large human artefacts, can influence the weather changes and evolutions; but they also affect the social and the economic conditions, the general health status, the density of human settlements, the level of pollution, which are strongly related to the epidemics developments and diffusions.
Once it is obtained and validated, a powerful tool for previsions of actual scenarios of infections will be available. Moreover, an approach to the control, acting on the habits and the local conditions as well as on the population migrations and on the long distance travels, can be followed, making use of optimal control techniques which can easily take into account also resources limitations.
According to the state of the art shortly described above, at the moment it is possible to find in literature a lot of contribution for what concerns epidemics modelling for almost all the known infective viruses, with deep analysis of regional cases for specific diseases. The approaches usually address the population, the different conditions of people with respect to the infection, the diffusivity of the epidemic based on individuals¿ contacts and the possible intervention actions of educational, behavioural and medical (vaccine and or drugs) type.
The parameters of the models can take into account environmental characteristics, often assumed as average conditions of the place or assumed with characteristic periodic behaviours, typically seasonal. The effects of climate changes or extreme weather conditions, when they are considered, are introduced changing the parameters values or adding specific terms for taking into account the peculiar effects. Despite the existence of more and more sophisticated climate models able to describe the short as well as long time dynamics of the weather and the possible changes caused by human factors, epidemiologists which want to adapt their models to climate characteristics and evolution, usually work at steady state, choosing one configuration, real, to analyse actual situations, or supposed (rise of temperature, excessive dry or rainy season, etc.), for predictive purposes.
The present project aims at integrate into a unique mathematical model both the climate and the epidemics evolutions; this can lead to a more powerful model which can provide the description of contagious diseases expressed with respect to time, as usual, but also as a spatial function, able to model and predict also the diffusion among different populations in different areas.
The integration is planned to be actuated following an incremental procedure. At a first step, the epidemiological models are going to be extended including the spatial dimension, so to be able to describe the propagation among areas along with the time evolution. This phase is introduced because is the one in which, mathematically, the dynamics are transformed from ordinary differential equations into partial differential equations. A second step goes toward the introduction of climate models, starting from local regions and moving to continental level, using them as the input of the epidemics descriptions. In this phase the climate and epidemics models are weakly coupled, so that the disease dynamics make use of real time data from climate ones, updating continuously the parameters. The third phase concerns the actual and full integration of the two kind of models, so that also the interactions between the state variables that describe the two systems can be considered.
An important note is that being the available models, for the two phenomena, of different complexity and dimensions, each step of the integration will obviously go from smaller to higher dimensions as well as from easier to more complex descriptions.
Each of these phases contains and represents an improvement of knowledge.
In fact, it is possible to find in literature models which aim at introducing epidemiological interactions between populations, but the proposed approaches are of two kinds: one involves very small numbers of populations, and the description is equivalent to the one of a single group simply with a higher order of the models, maintaining the analysis for the time evolutions only; the other one considers large numbers of populations and the relative interactions, but the systems are usually described as networks, with the nodes representing the populations, and the edges the interactions between them. In any case one can get a map of virus transmission, losing the time evolution in each populations in terms of number of infected and other classes. The result of the first step goes over these partial characterizations, making possible the description of the instantaneous number of each population class over the considered area, possible because of the partial differential equation based mathematical approach.
Also the second phase contains possible improvements, since instead of using predetermined climate cases in the epidemics diffusion models, the present project intends to connect the evolution of the two models exchanging data, so being able to consider instantaneously the effects of the climate in virus diffusions, allowing to capture the transients too.
The final goal is the most relevant improvement, being an actual innovative result in the scenario of the evolution of epidemics modelling correlated to climate conditions, for short time prediction, and climate variations for long time considerations.
Finally, making use of the mathematical models developed, optimal intervention actions can be designed, making use of optimal control theory based approaches, introducing also resources limitations and predetermined budgets.