Epidemic as a natural process

Abstract

Mathematical epidemiology is a well-recognized discipline to model infectious diseases. It also provides guidance for public health officials to limit outbreaks. Nevertheless, epidemics take societies by surprise every now and then, for example, when the Ebola virus epidemic raged seemingly unrestrained in Western Africa. We provide insight to this capricious character of nature by describing the epidemic as a natural process, i.e., a phenomenon governed by thermodynamics. Our account, based on statistical mechanics of open systems, clarifies that it is impossible to predict accurately epidemic courses because everything depends on everything else. Nonetheless, the thermodynamic theory yields a comprehensive and analytical view of the epidemic. The tenet subsumes various processes in a scale-free manner from the molecular to the societal levels. The holistic view accentuates overarching procedures in arresting and eradicating epidemics.

On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models

“…Such terms deviate the solution trajectory from the linear behavior about the equilibrium points. See, for instance, [5][6][7][8][9][10][11][12][13][14] and also [16][17][18][19][20][21] and some of the references therein. Example 1.…”

“…Proof. Note from (13) and (36) that the controllability gramian of the current linearized system G c[0,t * ] (A(t) , b(t)) is kept non-singular if that of its linearized counterpart G c0[0,t * ] (A 0 , b 0 ) is non-singular for all t * > 0 and, furthermore,G c0[0,t * ] (A 0 , b 0 ) = G c[0,t * ] (A(t), b(t)) − G c0[0,t * ] (A 0 , b 0 ) has a sufficiently…”

“…The background literature on epidemic models is very abundant, including the use of either vaccination or treatment controls as well as combinations of both types of controls. See, for instance, [5][6][7][8][9][10][11][12][13][14] and the references therein. Such controls may reduce the value of the basic reproduction number related to the case of absence of controls, so the average number of contagions per each primary infectious case, and they are also able to change the components of the equilibrium points, that is the numbers of each subpopulation at the equilibrium, and the rates the convergence to such equilibrium points.…”

“…Some of the models introduce appropriate either prediction or entropy tools or game theory to discuss the increase of disorder associated to them. See, for instance [11][12][13][14]. In particular, the entropy aspects are focused on deciding the various probabilities of different steady-state behaviors or to elucidate if the mathematical model is working properly, that is, if the entropy is non-negative [11].…”

Prediction of curve flattening time for COVID-19 infected countries using trends from recovered countries

“…With the outbreak of COVID-19, the researchers have shown interest in developing the prediction model of the pandemic curve. Every pandemic (or epidemic) is characterised by a typical sigmoid curve [10] which flattens at the end indicating the pandemic-free situation. The models generally used to predict the pandemic situation mainly attempt to fit these curves.…”