Mathematical analysis and optimal control applied to the treatment of leukemia

Khatun, M. S.; Biswas, Md. Haider Ali

doi:10.1007/s12190-020-01357-0

Cited by 13 publications

(13 citation statements)

References 25 publications

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“…Mathematical modelling aims at the mathematical representation of various biological processes such as wound healing, morphogenesis, blood-cell production and dynamics of infectious diseases, using techniques and tools of applied mathematics [5,6]. There exist a number of models for infectious diseases as well as chronic diseases; as for compartmental models and optimal control problem, starting from the very classical SIR model to more complex proposals [7][8][9]. The classical SIR type compartmental model was first introduced by Kermack and McKendrick in 1927 [10].…”

Section: Introductionmentioning

confidence: 99%

Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak

Biswas¹,

Islam²,

Akter³

et al. 2020

Computer Modeling in Engineering &Amp; Sciences

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COVID-19 is one of the most highly infectious diseases ever emerged and caused by newly discovered severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It has already led the entire world to health and economic crisis. It has invaded the whole universe all most every way. The present study demonstrates with a nine mutually exclusive compartmental model on transmission dynamics of this pandemic disease (COVID-19), with special focus on the transmissibility of symptomatic and asymptomatic infection from susceptible individuals. Herein, the compartmental model has been investigated with mathematical analysis and computer simulations in order to understand the dynamics of COVID-19 transmission. Initially, mathematical analysis of the model has been carried out in broadly by illustrating some well-known methods including exactness, equilibrium and stability analysis in terms of basic reproduction number. We investigate the sensitivity of the model with respect to the variation of the parameters' values. Furthermore, computer simulations are performed to illustrate the results. Our analysis reveals that the death rate from coronavirus disease increases as the infection rate increases, whereas infection rate extensively decreases with the increase of quarantined individuals. The quarantined individuals also lead to increase the concentration of recovered individuals. However, the infection rate of COVID-19 increases more surprisingly as the rate of asymptomatic individuals increases than that of the symptomatic individuals. Moreover, the infection rate decreases significantly due to increase of self-immunity rate.

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Section: Introductionmentioning

confidence: 99%

Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak

Biswas¹,

Islam²,

Akter³

et al. 2020

Computer Modeling in Engineering &Amp; Sciences

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show abstract

“…We perform mathematical analysis [ 22 ] of the model (2.2). We discuss the boundedness and non-negativity analysis, and determining the basic reproduction number for the model in the following manner.…”

Section: Mathematical Model Of Covid-19mentioning

confidence: 99%

Modeling the dispersal effect to reduce the infection of COVID-19 in Bangladesh

Kabir¹,

Gani²,

Mandal³

et al. 2020

Sensors International

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In this paper, we propose a four compartmental model to understand the dynamics of infectious disease COVID-19. We show the boundedness and non-negativity of solutions of the model. We analytically calculate the basic reproduction number of the model and perform the stability analysis at the equilibrium points to understand the epidemic and endemic cases based on the basic reproduction number. Our analytical results show that disease free equilibrium point is asymptotically stable (unstable) and endemic equilibrium point is unstable (asymptotically stable) if the basic reproduction number is less than (greater than) unity. The dispersal rate of the infected population and the social awareness control parameter are the main focus of this study. In our model, these parameters play a vital role to control the spread of COVID-19. Our results reveal that regional lockdown and social awareness (e.g., wearing a face mask, washing hands, social distancing) can reduce the pandemic of the current outbreak of novel coronavirus in a most densely populated country like Bangladesh.

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“…[34] analyzed and discussed about the very recent pandemic disease called COVID-19 that have killed about 4.5 million people already. Khatun and Biswas [35] worked with the leukemia mostly known as blood cell disease and applied control policy to minimize the disease. Mahmud [20] discussed about the Tuberculosis and HIV, their infection in Bangladesh.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Strategy to Reduce the Infection of Pandemic HIV Associated with Tuberculosis

Biswas

Samad

Parvin

et al. 2022

CBMS

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Tuberculosis (TB) and HIV/AIDS has become hazardous among communicable diseases and so as their co-infection in present era. HIV virus gradually weakens immune system in human body, and then TB infects with the assist of HIV/AIDS at any stage of the total infectious period. Today, HIV and tuberculosis (TB) are the main causes of mortality from infectious and chronic diseases. In this Study, we manifest a compartmental co-infection model including HIV and TB on the basis of their characteristics of disease transmission. The model is divided into 10 compartments, each with its own set of nonlinear ordinary differential equations. Using the Pontryagin's Maximum Principle, we investigate the existence of state variables, objective functional and optimum control plans. Identifying the most effective ways for reducing infection among the individuals, the optimal control techniques like vaccination control and treatment control measures are applied. The goal of this study is to lower the rate of HIV-TB co-infection and the cost of treatment. Another objective is to find the better control strategy to prevent HIV/AIDS that invites other pathogen in human body by gradual loosing of immunity. We carried out the investigation both analytically and numerically to divulge the effectiveness of the vaccination and treatment control to lessen the HIV and TB infection among the individuals.

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Mathematical analysis and optimal control applied to the treatment of leukemia

Cited by 13 publications

References 25 publications

Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak

Modelling the Effect of Self-Immunity and the Impacts of Asymptomatic and Symptomatic Individuals on COVID-19 Outbreak

Modeling the dispersal effect to reduce the infection of COVID-19 in Bangladesh

Optimal Control Strategy to Reduce the Infection of Pandemic HIV Associated with Tuberculosis

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