Optimal Intervention Strategies for a SEIR Control Model of Ebola Epidemics

Abstract

A SEIR control model describing the Ebola epidemic in a population of a constant size is considered over a given time interval. It contains two intervention control functions reflecting efforts to protect susceptible individuals from infected and exposed individuals. For this model, the problem of minimizing the weighted sum of total fractions of infected and exposed individuals and total costs of intervention control constraints at a given time interval is stated. For the analysis of the corresponding optimal controls, the Pontryagin maximum principle is used. According to it, these controls are bang-bang, and are determined using the same switching function. A linear non-autonomous system of differential equations, to which this function satisfies together with its corresponding auxiliary functions, is found. In order to estimate the number of zeroes of the switching function, the matrix of the linear non-autonomous system is transformed to an upper triangular form on the entire time interval and the generalized Rolle's theorem is applied to the converted system of differential equations. It is found that the optimal controls of the original problem have at most two switchings. This fact allows the reduction of the original complex optimal control problem to the solution of a much simpler problem of conditional minimization of a function of two variables. Results of the numerical solution to this problem and their detailed analysis are provided.

Optimal Treatment Strategies for Control Model of Psoriasis

“…Hence, we obtain the Cauchy problem, and as a corollary of the corresponding Existence and Uniqueness Theorem ( [9]), its solutions will be defined, generally speaking, locally, in some neighborhood of value t = 0. As it follows from [6,7], it is important to find restrictions for the coefficients of the equations of system (5.14) at which there exist solutions of Cauchy problem (5.14),(5.16) defined on the entire in-…”

“…For this, we use system (4.11), which is a linear non-autonomous homogeneous system of differential equations. To analyze this system, we apply the ideas presented in [6,7].…”

Optimal control problem for a seir type model of ebola epidemics

“…It is possible to find the best optimal strategies or preventives measures and corresponding epidemic outcomes by computer simulation of the model with specific initial conditions over a given time interval. Motivated by the Dallas Ebola case, we started working on the creation of a mathematical deterministic control model describing the spread of Ebola virus in the affected countries and published two papers [3,4]. Thus, our paper [3] contains a fairly complete review of works related to mathematical modeling of the spread of Ebola epidemics using SIR and SEIR type compartmental models.…”

“…Motivated by the Dallas Ebola case, we started working on the creation of a mathematical deterministic control model describing the spread of Ebola virus in the affected countries and published two papers [3,4]. Thus, our paper [3] contains a fairly complete review of works related to mathematical modeling of the spread of Ebola epidemics using SIR and SEIR type compartmental models. This paper is a continuation and further development of our studies presented in [3].…”

“…Thus, our paper [3] contains a fairly complete review of works related to mathematical modeling of the spread of Ebola epidemics using SIR and SEIR type compartmental models. This paper is a continuation and further development of our studies presented in [3]. Our goal is to minimize the sum of total fractions of exposed and infected individuals and also the total weighted cost of intervention control constraints over a given time interval.…”