Optimizing infection trajectories: Innovation in Controllability of Nonlinear SIR Model

Omar Zakary; Sara Bidah; Mostafa Rachik

doi:10.17488/RMIB.45.2.9

Authors

Omar Zakary Hassan II University of Casablanca, Faculty of sciences Ben M'Sik, Morocco https://orcid.org/0000-0003-0176-8233
Sara Bidah Hassan II University of Casablanca, Faculty of sciences Ben M'Sik, Morocco
Mostafa Rachik Hassan II University of Casablanca, Faculty of sciences Ben M'Sik, Morocco

DOI:

https://doi.org/10.17488/RMIB.45.2.9

Keywords:

controllability, control theory, infectious diseases, nonlinear models, SIR model

Abstract

Managing infections within populations poses significant challenges, particularly in achieving controllability over nonlinear models within epidemiological systems. In this study, the challenge is addressed by introducing a novel control function tailored to enhance the management of infections. The approach revolves around leveraging a nonlinear SIR epidemiological model, enabling the derivation of explicit solutions and fine-tuning of control parameters to align with predefined objectives. Specifically, the focus lies on guiding the number of infected individuals towards a predetermined threshold at a specified time for all initial values. Through rigorous numerical simulations, the effectiveness of the proposed control strategy in achieving greater controllability and regulating the spread of infection over time is depicted, For example, our simulations show that starting with an initial infected population of 150 individuals in a population of 25,150, the control strategy can reduce the number of infected individuals to below 40 within 30 days. The quantitative results presented underscore the efficacy of the approach, highlighting its potential to significantly impact disease management strategies.

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