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Author: search.filters.author.Das, Dhiraj KumarSubject: search.filters.subject.Fractional-order optimal control

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    Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability
    (Elsevier, 2022-08) Das, Dhiraj Kumar
    Hand, foot and mouth disease (HFMD) is highly contagious and occurs primarily among children under the age of five. Analysis of transmission dynamics of infectious diseases is essential to prevent the adverse effects caused by the diseases. The current study presents a fractional-order SEIR-type epidemic model to investigate the dynamics of HFMD transmission. The biological feasibility of the proposed model system is demonstrated from an epidemiological perspective. The basic reproduction number, R0, is obtained through the next-generation matrix approach. Around the feasible equilibrium points, the asymptotic dynamics of the proposed model system are examined, both at local and global levels. It is found that, the model undergoes transcritical bifurcation at R0 = 1. As a result, R0 plays the role of threshold in determining the future course of the disease. The optimal treatment control of fractional epidemic models are less explored. Here, an optimal control problem is formulated considering a time-dependent treatment measure u(t) both in exposed and infected classes. The findings are also visualized and verified by simulating the model using some feasible parameter values, from which it can be concluded that fractional-order gives better results. A gradual decrease in the total cases as well as in the peak is observed in the presence of treatment control. Further, we extend the study in a stochastic environment with the help of white noise and investigate the stochastic stability of the endemic equilibrium point. Finally, parameters defining the threshold quantity R0 are scaled with the normalized forward sensitivity index.
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    Complex dynamics and fractional-order optimal control of an epidemic model with saturated treatment and incidence
    (World Scientific, 2023) Das, Dhiraj Kumar
    In this study, we have developed a novel SIR epidemic model by incorporating fractional-order differential equations and utilizing saturated-type functions to describe both disease incidence and treatment. The intricate dynamical characteristics of the proposed model, encompassing the determination of the conditions for the existence of all possible feasible equilibria with their local and global stability criteria, are investigated thoroughly. The model undergoes backward bifurcation with respect to the parameter representing the side effects due to treatment. This phenomenon emphasizes the critical role of treatment control parameters in shaping epidemic outcomes. In addition, to understand the optimal role of the treatment in mitigating the disease prevalence and minimizing the associated cost, we investigated a fractional-order optimal control problem. To further visualize the analytical results, we have conducted simulation works considering feasible parameter values for the model. Finally, we have employed local and global sensitivity analysis techniques to identify the factors that have the greatest potential to reduce the impact of the disease.
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    Modeling and analysis of Caputo-type fractional-order SEIQR epidemic model
    (Springer, 2023-11) Das, Dhiraj Kumar
    In this research, a susceptible-exposed-infected-quarantine-recovered-type epidemic model containing fractional-order differential equations is suggested and examined in order to better understand the dynamical behavior of the infectious illness in the presence of vaccination and treatments. The non-negative and bounded solutions of our proposed model are examined for existence and uniqueness. We investigate the explicit formulation of a threshold , often known as the basic reproduction number, using the next-generation matrix technique. Depending on the value of , one endemic equilibrium exists and is stable for , and one disease-free equilibrium (exist for all values of ) is stable for . This article has also noticed the emergence of a transcritical bifurcation. The relevance of using vaccination and treatments as controls has been met by formulating a fractional-order optimal control problem. The resulting theoretical conclusions are supported by a few numerical simulations. Ultimately, a global sensitivity analysis is carried out to identify the parameters that have the greatest influence.