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    Local and global stability analysis of dengue disease with vaccination and optimal control
    (2021-10-01)
    Chamnan, Anusit
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    Tang, I. Ming
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    Dengue fever is a disease that has spread all over the world, including Thailand. Dengue is caused by a virus and there are four distinct serotypes of the virus that cause dengue DENV‐1, DENV‐2, DENV‐3, and DENV‐4. The dengue viruses are transmitted by two species of the Aedes mosquitoes, the Aedes aegypti, and the Aedes albopictus. Currently, the dengue vaccine used in Thailand is chimeric yellow tetravalent dengue (CYD‐TDV). This research presents optimal control which studies the vaccination only in individuals with a documented past dengue infection (seropositive), regardless of the serotypes of infection causing the initial infection by the disease. The analysis of dengue transmission model is used to establish the local asymptotically stabilities. The property of symmetry in the Lyapunov function an import role in achieving this global asymptotically stabilities. The optimal control systems are shown in numerical solutions and conclusions. The result shows that the control resulted in a significant reduction in the number of infected humans and infected vectors.
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    The Effect of Media in Mitigating Epidemic Outbreaks: The Sliding Mode Control Approach
    (2022-05-01)
    Ever since the World Health Organization gave the name COVID-19 to the coronavirus pneumonia disease, much of the world has been severely impact by the pandemic socially and economically. In this paper, the mathematical modeling and stability analyses in terms of the susceptible–exposed–infected–removed (SEIR) model with a nonlinear incidence rate, along with media interaction effects, are presented. The sliding mode control methodology is used to design a robust closed loop control of the epidemiological system, where the property of symmetry in the Lyapunov function plays a vital role in achieving the global asymptotic stability in the output. Two policies are considered: the first considers only the governmental interaction, the second considers only the vaccination policy. Numerical simulations of the control algorithms are then evaluated.
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    Simplified modelling and backstepping control of the long arm agricultural rover
    (2020-12-01) ;
    Boksuwan, Sungwan
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    Chesof, Abdulhafiz
    This paper presents the development of the simplified modelling and control of a long arm system for an agricultural rover, which also extends the modelling methodology from the previous work. The methodology initially assumes a flexible model and, through the use of the integral-based parameter identification method, the identified parameters are then correlated to an energy function to allow a construction of the friction induced nonlinear vibration model. To also capture the effect of the time delay, a delay model was also considered in the form of a second order delay differential equation. Both families of models were applied to identify and characterise a specialised long arm system. The nonlinear model was found to give significant improvement over the standard linear model in data fitting, which was further enhanced by the addition of the time delay consideration. A backstepping controller was also designed for both model families. Results show that the delay model expends less control efforts than the lesser non-delay model.
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    Finite-Time Integral Backstepping Nonsingular Terminal Sliding Mode Control to Synchronize a New Six-Term Chaotic System and Its Circuit Implementation
    This work presents the finite-time synchronization of a new six-term chaotic system with only stable equilibria and its circuitry implementation. The chaotic system is designed in such a way that its complex dynamical behavior, including hidden attractors, can be adjusted through only one parameter, whilst allowing transformation to chaotic flows via invariant transformations. A finite-time chaotic synchronizer is designed via a nonsingular terminal integral backstepping sliding mode controller, with reduced theoretical finite-time convergence, and a modified sliding surface, to accommodate analog circuitry implementations. A comparison between the proposed controller against conventional integral backstepping sliding mode controller showed that active synchronization is achieved in finite time. Finally, analog circuitry implementation for both open-loop and closed-loop configurations is realized via commercially available active components such as LF357 and AD633. The descriptive circuitry equations for both configurations are designed to mimic the actual governing control equations for simplicity and ease of circuit troubleshooting. The workability of both configurations was tested in OrCAD PSpice. Results show that the master and slave systems were found to be in synchronization with less than 0.95% maximum errors.
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    Mathematical modeling and optimal control of the hand foot mouth disease affected by regional residency in Thailand
    (2021-11-01) ;
    Tang, I. Ming
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    Dubois, Marc Antoine
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    Hand, foot and mouth disease (HFMD) is a virulent disease most commonly found in East and Southeast Asia. Symptoms include ulcers or sores, inside or around the mouth. In this research, we formulate the dynamic model of HFMD by using the SEIQR model. We separated the infection episodes where there is a higher outbreak and a lower outbreak of the disease associated with regional residency, with the higher level of outbreak occurring in the urban region, and a lower outbreak level occurring in the rural region. We developed two different optimal control programs for the types of outbreaks. Optimal Control Policy 1 (OPC1) is limited to the use of treatment only, whereas Optimal Control Policy 2 (OPC2) includes vaccination along with the treatment. The Pontryagin’s maximum principle is used to establish the necessary and optimal conditions for the two policies. Numerical solutions are presented along with numerical sensitivity analyses of the required control efforts needed as the control parameters are changed. Results show that the time t<inf>max</inf> required for the optimal control effort to stay at the maximum amount u<inf>max</inf> exhibits an intrinsic logarithmic relationship with respect to the control parameters.
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    Event-triggered based composite observer-oriented quantized truncated predictive tracking control for Markovian jump delay systems
    (2025-06-01)
    Shobana, N.
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    Mohammadzadeh, Ardashir
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    Sakthivel, R.
    This study encapsulates the multifaceted nature of attaining precise state tracking objectives in Markovian jump delay systems by encompassing a control technique related to delay compensation, fault tolerance, disturbance suppression and mismatch quantization. In brief, a quantized truncated predictive tracking control technique is implemented to achieve enhanced tracking outcomes by attenuating the influence of time-delays and mismatch quantization. Additionally, as a means of preventing transmission burden in the observer channel, an event-triggering-based composite generalized extended state observer is formulated to offer concurrent evaluations of plant states, actuator faults and external disturbances to the control device. Altogether, an event-triggered composite generalized extended state observer-oriented quantized truncated predictive tracking control algorithm is proposed with the objective of obtaining preferential tracking results despite the detrimental aspects. Specifically, by implying delay-dependent Lyapunov–Krasovskii functionals, we delineate the necessities for ensuring the stochastic stability of the specified system, detailed by linear matrix inequalities. Furthermore, the credibility of the examined findings is affirmed through graphical plots of numerical simulations.
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    Optimal control of the dengue dynamical transmission with vertical transmission
    (2019-12-01) ;
    Tang, I. Ming
    ;
    Dengue disease is found in tropical and subtropical regions around the world. Dengue virus is the cause of dengue fever, dengue hemorrhagic fever, and dengue shock syndrome. It consists of 4 serotypes: DEN-1, DEN-2, DEN-3, and DEN-4. There are two modes of transmission for dengue virus in mosquito: horizontal transmission and vertical transmission. The mosquito can be infected when it bites an infectious human by horizontal transmission, but there can also be vertical transmission through sexual contact with an infected mosquito. This research presents a control mechanism based on our previously developed dengue model with vertical transmission. The two policies, namely vaccination and insecticide administration (Policy 1) and isolation and insecticide administration (Policy 2) are considered. The use of Pontryargin’s maximum principle allowed necessary and optimality conditions, thus facilitating the optimal control to be developed. Numerical solutions of our control systems and the conclusions of our two policies are presented.
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    Synchronization of a Seven-Term Chaotic 4D System Using a Simplified Fixed-Time Adaptive Integral Nonsingular Terminal Sliding Mode Control and Its Circuit Realization
    This work presents an adaptive gain fixed-time synchronization of a seven-term hyperchaotic 4D system, along with its analog circuitry realizations. To facilitate a simplistic circuit realization of the closed loop system, the control design process initiates with the design of a novel, simplified fixed-time stability lemma that gives a lower convergence time, while being easier to compute. A nonlinear, fixed-time adaptive-gain nonsingular terminal sliding mode controller was then designed to synchronize the hyperchaotic 4D system. Theoretical analyses successfully achieved fixed-time synchronization, and computer simulations verified the achievement of zero-error convergence across all states within 1 second, irrespective of the initial conditions and even in the presence of significant parameter and disturbance changes. Analog circuitry implementations of the adaptive gain fixed-time chaotic synchronization configuration were realized using commercially available components, for instance, LF357 and AD633. The circuit equations were devised to replicate those used in the controller, with the goal of facilitating troubleshooting by ensuring simplicity. Electronics workability was tested using PSPICE simulation program. The results demonstrated that active synchronization was achieved in fixed time with less than 1% error across the states in the presence of disturbances. Finally, the developed fixed-time chaotic synchronization was applied to a secure communication system. The results indicate that the original and recovered messages exhibit a high degree of similarity to each other after a fixed duration of 1 second.
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    Global stability of the transmission of hand-foot-mouth disease according to the age structure of the population
    (2021-01-01)
    Lamwong, Jiraporn
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    Tang, I. Ming
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    This study investigates a transmission model of Hand-Foot-Mouth disease (HFMD) where the age structure of the population is taken into account. Most infections in Thailand occur among children below the age of 10 years, whose immunity to HFMD is lower than people of age greater than 10 years. Therefore, a mathematical model was developed in which the population was separated into two groups with respect to age: one comprised of children aged less than 10 years, and another comprised of the rest of the population. The reproductive number was obtained by the next-generation matrix approach. Global asymptotical stability of the developed model was assured using Lyapunov’s direct method. The model was validated by showing that the 2D and 3D trajectories of the numerical solutions for the different sub-population groups converged to the endemic equilibrium states when the reproduction number was greater than one, thus supporting the theoretical conclusions. Results show that the time series behaviors of the different normalized populations groups converge to the disease-free state when the values of the parameters are such that the basic reproductive number is 0.591481 (i.e., less than one) and to an endemic state when the values of the parameters are such that R<inf>0</inf> = 54.4523 and R<inf>0</inf> = 192.575 R = (i.e. greater than one). The results of this study can suggest ways for reducing the outbreak of this disease.
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    The Lyapunov Analyses of MERS-Cov Transmission in Thailand
    (2019-01-01)
    Lamwong, Jiraporn
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    Tang, I. Ming
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    This work investigates the transmission model of MERS-Cov using SEIR model which divides the total human population into four subclasses: susceptible, exposed, infected and recovered. Two * equilibrium points were exhibited: the disease-free equilibrium E1 and the endemic equilibrium E<sup>*</sup> 2. The basic reproduction number was computed via the next generation method. Two types of global stability of these equilibrium points were investigated through the theory of Lyapunov. Specifically, the exponential stability was investigated using a square type Lyapunov candidate function; while the asymptotic stability was investigated through a Logarithm type Lyapunov candidate function. It is theoretically shown that, when the reproductive number is less than unity. The disease-free equilibrium state is globally asymptotically stable, and the endemic equilibrium state is globally asymptotically stable if the reproductive number is greater than unity. Numerical results with parameters obtained from the previous work also illustrates the global asymptotical stability of the MERS-Cov system. These results can further be used for the design of a controller that drives the MERS-Cov system and the effective control reproductive number is less than 1 so that the stability of the controlled system would be similar to that of the uncontrolled disease-free system.