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Articles 1 - 6 of 6
Full-Text Articles in Control Theory
Optimal Control And Bifurcation Analysis Of A Predator–Prey Model With Self-Limiting Growth And Predator Disease, Dipo Aldila, Muhammad Akmal Fasya, Bevina D. Handari, Chidozie Williams Chukwu, Olumuyiwa James Peter
Optimal Control And Bifurcation Analysis Of A Predator–Prey Model With Self-Limiting Growth And Predator Disease, Dipo Aldila, Muhammad Akmal Fasya, Bevina D. Handari, Chidozie Williams Chukwu, Olumuyiwa James Peter
Mathematical Modelling and Numerical Simulation with Applications
We propose and analyze an eco-epidemiological predator–prey model that incorporates self-limitation and disease transmission within the predator population. The model is formulated as a system of ordinary differential equations describing logistic prey growth under the interspecific interaction with the predator. On the other hand, the predator population is divided into susceptible and infected classes, whose growth is constrained by prey availability. Three biologically relevant equilibria are identified: predator extinction, disease-free coexistence, and coexistence with endemic disease. The existence and stability of these equilibria are determined by key ecological and epidemiological thresholds, including the basic reproduction number. Using numerical continuation methods, …
Optimal Control Strategies For Infectious Diseases: A Numerical Simulation Approach, M. Abu Salek, Jannatun Nayeem, Romana Yesmin, M. Haider Ali Biswas, M. Humayun Kabir
Optimal Control Strategies For Infectious Diseases: A Numerical Simulation Approach, M. Abu Salek, Jannatun Nayeem, Romana Yesmin, M. Haider Ali Biswas, M. Humayun Kabir
Mathematical Modelling and Numerical Simulation with Applications
Various infectious diseases, such as Tuberculosis and Hepatitis B virus (HBV), caused by Mycobacterium bacteria and hepatitis B virus, respectively, pose serious threats worldwide. This paper examines the spread of these diseases using a mathematical model that incorporates control measures, including vaccination and awareness programs. We use a system of differential equations with control variables and apply Pontryagin's principle to determine optimal control strategies. The stability of the Disease Free Equilibrium (DFE) has been analysed and demonstrated to be both locally and globally asymptotically stable when the basic reproduction number remains below unity, thereby ensuring disease elimination. Furthermore, the Endemic …
Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan
Dynamical Analysis And Optimal Control Of The Mpox Transmission Model With Stratified Susceptibility, Tuhfatul Janan, Fatmawati Fatmawati, Cicik Alfiniyah, Santi Martini, Dipo Aldila, Agus Hasan
Mathematical Modelling and Numerical Simulation with Applications
This study develops a mathematical model of Mpox transmission that combines stratified susceptibility (low-risk and high-risk groups) with vaccinated and asymptomatically infected compartments. The analysis of the model begins with examining the well-posedness, boundedness, and nonnegativity conditions for the solutions. The local stabilities of the equilibria are examined through the Jacobian matrix and phase plane analysis, while the global stabilities are provided through Lyapunov functions. The estimated parameters are verified using epidemiological data on Mpox cases in the United States, with an MAPE of 2.20% and R_0 > 1, indicating that Mpox remains endemic. Sensitivity analysis indicates that the contact rate …
Optimal Control Of Stochastic Systems: A Numerical Study Of The Stochastic Linear Quadratic Regulator Framework, Gülşen Orucova Büyüköz, Yaprak Güldoğan Dericioğlu, Tuğçem Partal
Optimal Control Of Stochastic Systems: A Numerical Study Of The Stochastic Linear Quadratic Regulator Framework, Gülşen Orucova Büyüköz, Yaprak Güldoğan Dericioğlu, Tuğçem Partal
Mathematical Modelling and Numerical Simulation with Applications
Optimal control of stochastic linear systems is fundamental in control theory, with applications in robotics, finance, and engineering. The Stochastic Linear Quadratic Regulator (SLQR) derives optimal feedback laws via the Riccati equation but requires numerical discretization of the resulting stochastic dynamics. Despite extensive studies on numerical methods for stochastic differential equations, their performance within the SLQR framework remains insufficiently explored. This study compares two predictor–corrector schemes of different orders: the Order 1.0 Predictor-Corrector (PC) method and the Order 2.0 Weak PC method. A one-dimensional linear quadratic problem with a closed-form solution enables precise error evaluation against the analytical trajectory. Convergence …
Analysis And Numerical Investigation Of A Breast Cancer Treatment Model Incorporating Ketogenic Diet And Immune Boosters Via Optimal Control Theory, Kunnisai Muniroh, Ummu Habibah, Wuryansari Muharini Kusumawinahyu, Nur’Izzati Hamdan
Analysis And Numerical Investigation Of A Breast Cancer Treatment Model Incorporating Ketogenic Diet And Immune Boosters Via Optimal Control Theory, Kunnisai Muniroh, Ummu Habibah, Wuryansari Muharini Kusumawinahyu, Nur’Izzati Hamdan
Mathematical Modelling and Numerical Simulation with Applications
This paper develops a mathematical model to investigate breast cancer dynamics by incorporating tumor–immune interactions, ketogenic diet effects, and medical treatment. The model is formulated as a system of nonlinear ordinary differential equations and analyzed within an optimal control framework. Time-dependent control variables are introduced to represent treatment strategies aimed at minimizing tumor progression while reducing therapeutic costs. The model’s well-posedness is established through positivity and boundedness analysis. The necessary conditions for optimality are derived using Pontryagin’s Minimum Principle, resulting in a coupled system of state and adjoint equations. Numerical solutions are obtained using the fourth-order Runge–Kutta method combined with …
Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk
Dynamics And Optimal Intervention Strategies In A Shigellosis Transmission Model, Mehmet Gümüs, Shewafera Wondimagegnhu Teklu, Kemal Türk
Mathematical Modelling and Numerical Simulation with Applications
This research explores how water treatment contributes to limiting the transmission of Shigellosis, an infection caused by bacteria from the Shigella genus. A mathematical framework is formulated to evaluate the influence of protective strategies and water purification on the spread of the disease. To confirm the model's biological relevance, its well-posedness is investigated. The basic reproduction number $(\mathfrak{R}_0)$, a critical indicator of disease behavior, is derived using the matrix operator method. Findings indicate that if $\mathfrak{R}_01$, the infection persists, with the endemic equilibrium exhibiting local asymptotic stability. A comprehensive cost-effectiveness analysis reveals that combining environmental protection with water treatment represents …