A QUANTITATIVE ANALYSIS OF PREVENTIVE MEASURES TO MITIGATE THE INFECTIOUS DISEASES USING SIR MODEL BY OPTIMAL CONTROL TECHNIQUE

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Published: Apr 28, 2022
Keywords:
SIR Model Optimal control Vaccination as control Existence of the state Existence of the objective functional Pontryagin’s Maximunm Principle
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Jakia Sultana
Samiha Islam Tanni
Shamima Islam

Abstract

Optimal Control Problem with the state equations which describes the standard SIR Model is studied here. we considered the SIR Model with vaccination and without vaccination. We formulated an optimal control problem and derived necessary conditions. Existence of the state and the objective functional are also verified. We also characterized the optimal control by Pontryagin’s maximum principle which minimizes the number of infected individuals and cost of vaccination over some finite period. Whenever the vaccination is carried out for a long period of time, the simulated result effectively works for diseases with high transmission rate. Observations from the numerical simulation reveals that the infectious diseases are most successfully controlled whenever control strategies were adopted at early stages.

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Issue:
Vol. 5 No. 1 (2018): Volume 05, Issue 01, December-2018
Area :
Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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