Imprecise parameters for near‐optimal control of stochastic SIV epidemic model

Abstract

The change of parameters may influence the dynamic behaviors of epidemic diseases. Biological system parameters can also be changed due to diverse uncertainties such as lack of data and errors in the statistical approach. The problem of how to define and decide the optimal‐control strategies of epidemic diseases with imprecise parameters deserves further researches. The paper presents a stochastic susceptible, infected, and vaccinated (SIV) system that includes imprecise parameters. Firstly, we give the method of parameter estimates of the SIV model. Then, by using Ekeland's principle and Hamiltonian function, we obtain the sufficient conditions and necessary conditions of near‐optimal control of the SIV epidemic model with imprecise parameters. At last, numerical examples prove our theoretical results.

Probability analysis and near-optimal control for a stochastic epidemic treatment model with relapse

“…For a stochastic model, the nonuniqueness of an existent optimal control is a very challenging problem to explore. Hence, as a feasible possibility, many authors started to explore a near-optimal control problem for epidemic models [14][15][16], viral [17] and chemostat [18] models, where the hypothesizes are weaker. Therefore, we investigate a controlling approach for the following stochastic epidemic model [6] with relapse dS(t) = [µ − µS(t) − βS(t)I(t)]dt − σS(t)I(t)dB(t), dI(t) = [βS(t)I(t) − (µ + λ)I(t) + ρR(t)]dt + σS(t)I(t)dB(t)…”