Optimal control of the SIR model with constrained policy, with an application to COVID-19

The current study represents a survey on several modifications of compartment epidemic models with continuous and impulse control policies. The main contribution of the survey is the modification of the classical Susceptible Infected Recovered (SIR) model with the assumption that two types of viruses are circulating in the population at the same time. Moreover, we also take into consideration the network structure of the initial population in two-virus SIIR models and estimate the e ectiveness of protection measures over complex networks. In each model, the optimal control problem has been formalized to minimize the costs of the virus spreading and find optimal continuous and impulse antivirus controllers. All theoretical results are corroborated by a large number of numerical simulations.

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Optimal control of behaviour and treatment in a nonautonomous SIR model

International Journal of Dynamical Systems and Differential Equations ◽

10.1504/ijdsde.2021.10037984 ◽

2021 ◽

Vol 11 (2) ◽

pp. 108

Author(s):

Parthasakha Das ◽

Pritha Das ◽

Samhita Das

Keyword(s):

Optimal Control ◽

Sir Model

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Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2021004 ◽

2021 ◽

Author(s):

Jayanta Kumar Ghosh ◽

Prahlad Majumdar ◽

Uttam Ghosh

Keyword(s):

Optimal Control ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Transmission Rate ◽

Sir Model ◽

Logistic Growth ◽

Treatment Rate ◽

Globally Asymptotically Stable ◽

Susceptible Population ◽

Saturated Treatment

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point ( DFE ) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov - Takens bifurcation ( BT ) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

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Kontrol Optimal pada Model Epidemik SIR Penyakit Demam Berdarah

Indonesian Journal of Fundamental Sciences ◽

10.26858/ijfs.v4i2.7639 ◽

2018 ◽

Vol 4 (2) ◽

pp. 110

Author(s):

Katrina Pareallo ◽

Wahidah Sanusi ◽

Syafruddin Side

Keyword(s):

Optimal Control ◽

Yellow Fever ◽

Aedes Albopictus ◽

Minimum Principle ◽

Sir Model ◽

Distribution Model ◽

Control Factor ◽

System Of Differential Equations ◽

Dengue Vaccine ◽

Result Analysis

This study discusses about the optimal control on dengue fever distribution model using the minimum principle of Pontryagin. Dengue is a disease caused by dengue virus it transmitted by the female mosquitos species, namely Aedes aegeypti and Aedes Albopictus. Thus disease cause death if not treated seriously. The disease can be prevented by vaccine, called Chimeric Yellow Fever 17D-Tetravalent Dengue Vaccine(CYD-TDV). The discussion starts from determining the SIR model using the controls, determining the optimal control using the minimum principle of Pontryagin , the simulation using Maple software and the result analysis. In this study obtained the system of differential equations, optimal control equations, and graphs of the SIR model without using controls and using the control. Based on the results obtained concluded that by adding control factor to SIR model can minimize the number of infected individuals.

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