Feedback Linearization and Optimal Control of the Kermack-McKendrick Model for the Spread of Epidemics

Abstract

Using the feedback linearization method, a state feedback control for the two-dimensional Kermack-McKendrick model for the spread of epidemics is obtained. This form of the dynamical system is suitable to carry out a qualitative analysis of the model. An optimal control problem for a stochastic version of the model is also set up and solved explicitly in a particular instance.

On the inverse LQG homing problem

“…Therefore, the final time in this optimal control problem is indeed a random variable. See also Ionescu et al [1].…”

“…However, in the case of jump-diffusion processes, we can have u * (x) ≡ 0 in nontrivial problems. Indeed, assume that or [1,3). Let us define (3.5)…”

A stochastic model for computer virus propagation

“…proposed to explain the 2014 outbreak of the Ebola virus in West Africa. Ionescu et al [2] and Lefebvre [4] solved optimal control problems for stochastic versions of the classic Kermack-McKendrick model. Tong et al [12] also considered an optimal control problem based on this virus propagation model.…”

“…in the system defined in (2). In the next section, the deterministic model will be solved explicitly.…”

“…Deterministic model. In this section, we consider the system defined in (2). We can obtain an explicit solution for any choice of the constants k i , for i = 1, 2, 3.…”