Game dynamic model of optimal budget allocation under individual vaccination choice

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

“…Proof. Equation 21follows directly from (11) under the conditions (1)- (2). Condition (3) follows since one gets from (14)-(15) that x 0 = 0 implies that x(t * ) = x * 0 if:…”

“…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.…”

“…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.…”

“…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. The usual epidemic models are typically based on differential, difference or mixed equations which describe the coupled dynamics of the various subpopulation or, in general, they can include point and distributed delayed dynamics or to be also formulated in a stochastic framework, [7,8,11]. There are also studies for models of networks available which include different nodes which can represent different sets of interacting communities [14,15], which combined control strategies which take into account the communication links and population flows.…”

“…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].…”