Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth

Abstract

In this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control problems with various kinds of constraints including mixed control-state and state constraints. After presenting the new model and implementing the optimal control problems by means of a first-discretize-then-optimize method, numerical results for six scenarios are discussed and compared to an analytical optimal control law based on Pontrygin's minimum principle that allows to verify these results as approximations of candidate optimal solutions.

Optimal control of COVID-19 infection rate considering social costs

“…A similar finding was made for an SEIR type model applied to COVID-19 in [12] with control on the transition rate. An SEIR model with logistic population growth is considered in [16], where the control found by numerical optimization appears to approach a state where the disease is endemic in the population. An SEIR type model has been applied to COVID-19 in [5] with the infection rate controlled up until a vaccine is developed.…”

Optimal control strategy of SEIR endemic model with continuous age‐structure in the exposed and infectious classes

“…For numerical simulation of the optimal system, the state equations and the associated equations are solved using finite forward and backward schemes. The initial population of susceptible, exposed infected, and recovered were taken from the work of Thater et al, while for justification of parameter's values, see Table . The functions σ ( a ) and ξ ( a ) is assumed to be a fraction times e − a because the function e − a in addition to monotonicity possesses other important characteristics such as boundedness, positivity, and decay to zero at infinity.…”

“…The key idea of modeling epidemics is to provide a rational basis for policy makers to control the spread of a disease. Controlling the impact of such outbreaks, researchers try to investigate an effective strategy by setting an optimal control . In the context of optimal control of age‐structured model, Anita considered optimal harvesting in single equation.…”

Optimal control strategies for an age‐structured SEIR epidemic model

“…The classical SEIR models comprise of ordinary differential equations have been rigorously investigated for global analysis by many researchers 8,9 . Other researchers applied control theory to such type of models and derived some effective strategies 10,11 . Models of SEIR type consist of ODEs and PDEs (called mixed models) have also an extensive history.…”