Analysis of a mathematical model for tuberculosis with diagnosis

Egonmwan, A. O.; Okuonghae, D.

doi:10.1007/s12190-018-1172-1

Cited by 50 publications

(43 citation statements)

References 52 publications

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“…So, by considering the Eqs. (19) and (20), and by applying the recursive technique we obtained the succeeding results as below:…”

Section: Theorem 42mentioning

confidence: 99%

“…The TB model with global stability results was discussed by Liu et al in [28]. Egonmwan et al [19] developed a new TB model to explore the impact of treatment and diagnoses for both latent and active TB infective population. Zhang et al [42] proposed the TB mathematical model with hospitalized and non hospitalized infective classes and implemented the TB data of China to simulate the model.…”

mentioning

confidence: 99%

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A fractional model for the dynamics of tuberculosis infection using Caputo-Fabrizio derivative

Ullah¹,

Khan²,

Farooq³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

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In the present paper, we study the dynamics of tuberculosis model using fractional order derivative in Caputo-Fabrizio sense. The number of confirmed notified cases reported by national TB program Khyber Pakhtunkhwa, Pakistan, from the year 2002 to 2017 are used for our analysis and estimation of the model biological parameters. The threshold quantity R 0 and equilibria of the model are determined. We prove the existence of the solution via fixedpoint theory and further examine the uniqueness of the model variables. An iterative solution of the model is computed using fractional Adams-Bashforth technique. Finally, the numerical results are presented by using the estimated values of model parameters to justify the significance of the arbitrary fractional order derivative. The graphical results show that the fractional model of TB in Caputo-Fabrizio sense gives useful information about the complexity of the model and one can get reliable information about the model at any integer or non-integer case.

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“…So, by considering the Eqs. (19) and (20), and by applying the recursive technique we obtained the succeeding results as below:…”

Section: Theorem 42mentioning

confidence: 99%

mentioning

confidence: 99%

A fractional model for the dynamics of tuberculosis infection using Caputo-Fabrizio derivative

Ullah¹,

Khan²,

Farooq³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

View full text Add to dashboard Cite

show abstract

“…e number of research studies that employ mathematical modeling to study the dynamics of infectious disease has rapidly increased over the last two decades. e research foci in this area are ranging from the study of respiratory diseases such as measles, influenza, and tuberculosis; vector-borne diseases such as malaria, Ebola, zikav, and dengue; to sexually transmitted diseases such as HIV/AIDS (see for instance the works of Beay [23], Reynolds et al [24], Mitchell and Ross [25], Egonmwan and Okuonghae [26], Nkamba et al [27], Bakary et al [28], Irwan et al [29], Akgül et al [30], Ainisa et al [31], Carvalho et al [32], Omondi et al [33], and Chong et al [34]). Mathematical modeling is usually used to characterize the epidemiological parameters of disease during outbreaks and to evaluate the effectiveness and schedule of various prevention and control strategies, considering limited resource availability [35].…”

Section: Related Workmentioning

confidence: 99%

Control Policy Mix in Measles Transmission Dynamics Using Vaccination, Therapy, and Treatment

Jaharuddin

Bakhtiar

2020

International Journal of Mathematics and Mathematical Sciences

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This paper considers a deterministic model for the dynamics of measles transmission in a population divided into six classes with respect to the disease states: susceptible, vaccinated, exposed, infected, treated, and recovered. First, we investigate the dynamical properties of the SVEITR model such as its equilibrium points, their stability, and parameter sensitivity by applying constant controls. Criteria for determining the stability of disease-free and endemic equilibrium points are provided in terms of basic reproduction number. The model is then extended by incorporating vaccination, therapy, and treatment rates as time-dependent control variables representing the level of coverages. Application of Pontryagin’s maximum principle provides the necessary conditions that must be satisfied for the existence of optimal controls aiming at minimization of the number of exposed and infected individuals simultaneously with the control effort. Numerical simulations that were carried out using the backward sweep method and Runge–Kutta scheme suggest that optimal controls under moderate and high scenarios can effectively reduce the cases of measles. In particular, the moderate scenario that utilizes the existing coverage level of 86% for MCV1 and 69% for MCV2 can degrade the cost functional by 47% of the low scenario. Meanwhile, high scenario that takes the 2020 target of 96% as coverage only makes a slight difference in reducing the number of exposed and infected individuals.

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“…By considering effect of drugs, the mathematical models were proposed and analyzed the stability of the model [5][6][7][8]. Egonmwan et al [9][10][11] studied the model to analyze the stability of the model considering the effect of treatments.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Tuberculosis Epidemic Model with Saturated Infection Force

2020

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A mathematical model with saturated infection rate is studied incorporating the effect of treatment for Tuberculosis (TB) infected individuals. The model is studied to analyze the local stability of equilibriums by center manifold. The effect of treatment, namely chemoprophylaxis for exposed individuals and therapy for infectious individuals is investigated numerically. The numerical results show that the chemoprophylaxis treatment is more effective in decreasing the spread of TB epidemic. Otherwise it increases the healthy individuals.

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Analysis of a mathematical model for tuberculosis with diagnosis

Cited by 50 publications

References 52 publications

A fractional model for the dynamics of tuberculosis infection using Caputo-Fabrizio derivative

A fractional model for the dynamics of tuberculosis infection using Caputo-Fabrizio derivative

Control Policy Mix in Measles Transmission Dynamics Using Vaccination, Therapy, and Treatment

Stability Analysis of Tuberculosis Epidemic Model with Saturated Infection Force

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