Stability analysis and optimal control of a fractional human African trypanosomiasis model

Bonyah, Ebenezer; Gómez-Aguilar, J. F.; Adu, Augustina

doi:10.1016/j.chaos.2018.10.025

Cited by 38 publications

(23 citation statements)

References 14 publications

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“…The technique is one of the indirect methods, in which the differential equations from the maximum principle are numerically solved. This method is widely used in the solution of optimal control in recent years . The comparison with other methods is presented in Sana et al The conditioning of the problem and the nature of the approximations of the forward‐backward sweep method in optimal control have been analyzed; see McAsey et al…”

Section: Numerical Simulationmentioning

confidence: 99%

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Optimal control and stability analysis of an online game addiction model with two stages

Guo

2020

Math Meth Appl Sci

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In this paper, we establish a mathematical model of online game addiction with two stages to research the dynamic properties of it. The existence of all equilibria is obtained, and the basic reproduction number is calculated by the method of next‐generation matrix. The global asymptotic stability of disease‐free equilibrium (DFE) is proved by comparison principle, and the global asymptotic stability of endemic equilibrium (EE) is proved by constructing an appropriate Lyapunov function. Then we use the Pontryagin's maximum principle to find the optimal solution of the model, so that the number of infected people can be minimized. In numerical simulation, firstly, we validate the global stability of DFE and EE. Secondly, we consider three kind of control measures (treatment, isolation, and education) and divide them into four cases. The models with control and without control are solved numerically by using forward and backward sweep Runge‐Kutta method. In order to achieve the best control effect, we suggest that three kind of measures should be used simultaneously according to the optimal control strategy.

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Section: Numerical Simulationmentioning

confidence: 99%

“…Theorem 4. The objective function and the control set respectively given by (22) and (23) are subject to the state system (5.1). There exists an optimal control u * = (u *…”

Section: Existence Of the Optimal Controlmentioning

confidence: 99%

Optimal control and stability analysis of an online game addiction model with two stages

Guo

2020

Math Meth Appl Sci

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“…The combination of different control combinations, cases 1-4 are performed, and we concluded by activating the three controls at the same time can best reduce the number of infective individuals in Pakistan. In future work, we consider analyzing this model involving derivatives and integrals of noninteger order [23][24][25][26][27][28] and compare the results obtained.…”

Section: Resultsmentioning

confidence: 99%

Mathematical formulation of hepatitis B virus with optimal control analysis

Ullah

Khan

Gómez‐Aguilar

2019

Optim Control Appl Methods

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Summary Hepatitis B infection is a serious health issue and causes many deaths around the world. The aim of this paper is to develop a mathematical model with hospitalized population to explore the dynamics of this infection. Initially, we study the model without control and carried out all the basic properties and results including local and global stability. After that, we develop the model with suitable optimal control strategies and explore the necessary optimality conditions using the well known Pontryagin's maximum principle to minimize the spread of hepatitis B in a community. Finally, we present the numerical simulations of both with and without control models to illustrate the feasibility of the control strategy.

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“…Finally, they have supported their theoretical aspects with a numerical example. In addition to these studies, in the literature there are many papers demonstrate to model other epidemic models and special diseases such as modelling the spread of computer virus [9], stability analysis of a fractional human African trypanosomiasis model [10], a schistosomiasis disease model [11], a novel framework for blood vessels detection in retinal images [12], a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model [13], SIRI epidemic model with distributed delay and relapse [14], etc.…”

Section: Introductionmentioning

confidence: 99%

Analysis of an Epidemic Spreading Model with Exponential Decay Law

Yavuz¹,

Özdemir²

2020

Mathematical Sciences and Applications E-Notes

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Mathematical modeling of infectious diseases has shown that combinations of isolation, quarantine, vaccine, and treatment are often necessary in order to eliminate most infectious diseases. Continuous mathematical models have been used to study the dynamics of infectious diseases within a human host and in the population. We have used in this study a SIR model that categorizes individuals in a population as susceptible (S), infected (I) and recovered (R). It also simulates the transmission dynamics of diseases where individuals acquire permanent immunity. We have considered the SIR model using the Caputo-Fabrizio and we have obtained special solutions and numerical simulations using an iterative scheme with Laplace transform. Moreover, we have studied the uniqueness and existence of the solutions.

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Stability analysis and optimal control of a fractional human African trypanosomiasis model

Cited by 38 publications

References 14 publications

Optimal control and stability analysis of an online game addiction model with two stages

Optimal control and stability analysis of an online game addiction model with two stages

Mathematical formulation of hepatitis B virus with optimal control analysis

Analysis of an Epidemic Spreading Model with Exponential Decay Law

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