![]() the cumulative probability of infection vs. To do so, we consider the recent results obtained in relation to the use of the logistic approach by Loum et al. Materials and Methodsįirst, we must consider a reference statistics for a human to be infected. In this paper, we therefore extend a thermodynamic approach of complex systems to the analysis of epidemics by introducing entropy as a tool to predict the evolution of an infectious disease. ![]() Entropy has been proven to represent a fundamental key for the analysis of some biosystems. This results in finding the most probable macroscopic pathway realized by the greater number of microscopic paths compatible with the imposed constraints. He maximized the Shannon entropy for information in relation to the pathway followed in the thermodynamic phase space, by considering the probability subject to the actual constraints. In this context, we note that Jaynes developed a non-equilibrium statistical mechanics approach for the stationary state constraint, on the basis of the principle of maximum entropy. At present, there are a great number of estimators of the tail-index, but, a generic approach is required in order to generalize the statistical approach to complex systems, such as in the case of epidemics or pandemics.įurthermore, the spread of infection can be studied as the evolution of an open thermodynamic system. The existence of specific finite moments is closely related to the concept of a tail index, and its estimation is one of key problems in statistics. But, when the data are collected by a heavy-tailed distribution, the mathematical bases of the usual statistics is not satisfied. Indeed, the usual statistical approach is based on the Kolmogorov's law of large numbers which requires the existence of the first finite moment, and the Lyapunov's version of the central limit theorem assumes an existence of the finite moment of an order higher than two. Scientists and engineers have always searched for the best statistical distribution useful to predict the behavior of the systems under consideration. However, especially in the beginning of any epidemics we have only partial access to validated data also because the number of infected people is still rather small and follows a dynamic process. Traditionally, epidemiological analyses are based on sigmoidal models, which indeed are useful if the evolution of the epidemics follows well-established patterns. Consequently, it is fundamental to develop a reliable analytical approach that allows such predictive modeling. ![]() To implement effective public health measures in a timely manner and allocate scarce resources according to geographic need, it is very important to forecast the diffusion or spread of the infection amongst the population. Consequently, the interest in forecasting the diffusion of such global infectious disease threats is continuously increasing. Moreover, epidemics and pandemics can cause also significant, widespread economic hardship and potentially lead to social unrest. Some recent examples of pandemics are the 2003 SARS (Severe Acute Respiratory Syndrome), the 2014 West Africa Ebola epidemic, and the present COVID-19 caused by the coronavirus SARS-Cov-2. Indeed, epidemics can occur in a community or region by causing illness in excess of normal expectancy pandemics are no more than a large-scale global epidemic which determine a growth in morbidity and mortality over a wide geographic area. This is particularly true in epidemiology. Consequently, in any field of research, scientists, and engineers have always taken attention to find the best statistical distribution to predict the systems behavior. ![]() In the natural, social, economic, and physical sciences a large variety of phenomena are characterized by regularities, which can be analytically described by a defined statistical distribution. ![]()
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