Sensitivity Analysis of the Parameters of a Mathematical Model of Hepatitis B Virus Transmission

Abdulrahman, S; Akinwande, Niniuola Ifeoluwa; Awojoyogbe, Bamidele O.; Abubakar, Usman Yusuf

doi:10.13189/ujam.2013.010405

Cited by 10 publications

(9 citation statements)

References 27 publications

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“…Our main aim is continuous and discrete characterization of model (2). It is assumed that all the parameters are positive constants where the parameters and their explanations are provided in Table 1.…”

Section: Mathematical Model For Hbvmentioning

confidence: 99%

“…Chronic disease afects the liver ability to perform life-sustaining processes such as removing dangerous transmitted substances from the blood, collecting sugar levels, and converting it to useable energy forms [1]. Hepatitis B virus (HBV) is one of the world most serious health problems [2]. HBV has a large rate of deaths, both from acute and chronic infection [3].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Continuous and Discrete Stability Characterization of Hepatitis B Deterministic Model

Hussain

Khan

et al. 2022

Mathematical Problems in Engineering

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The hepatitis B infection is a global epidemic disease which is a huge risk to the public health. In this paper, the transmission dynamics of hepatitis B deterministic model are presented and studied. The basic reproduction number is attained and by applying it, the local as well as global stability of disease-free and endemic equilibria of continuous hepatitis B deterministic model are discussed. To better understand the dynamics of the disease, the discrete nonstandard finite difference (NSFD) scheme is produced for the continuous model. Different criteria are employed to check the local and global stability of disease-free and endemic equilibria for the NSFD scheme. Our findings demonstrate that the NSFD scheme is convergent for all step sizes and consequently reasonable in all respect for the continuous deterministic epidemic model. All the aforementioned properties and their effects are also proved numerically at each stage to show their mathematical as well as biological feasibility. The theoretical and numerical findings used in this paper can be employed as a helpful tool for predicting the transmission of other infectious diseases.

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Section: Mathematical Model For Hbvmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Continuous and Discrete Stability Characterization of Hepatitis B Deterministic Model

Hussain

Khan

et al. 2022

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…There are more than a dozen ways of conducting sensitivity analysis, all resulting in a slightly different sensitivity ranking" [15]. "Following [14], we used the normalized forward sensitivity index also called elasticity as it is the backbone of nearly all other sensitivity analysis techniques [15] and are computationally efficient" [16]. The normalized forward sensitivity index of the basic reproduction number, with respect to a parameter value, is given by: (12) The sensitivity indices of the basic reproductive number with respect to main parameters are arranged orderly in Table 1.…”

Section: Sensitivity Analysis Of Model Parametersmentioning

confidence: 99%

“…To prove the boundedness we use the method in []. To do so we use the fact the super-solutions of system 13 is written as: (16) are bounded on a finite time interval. System 17 can be written as; (17) The system is linear in finite time with bounded coefficients, then the super-solutions and is uniformly bounded.…”

Section: Proofmentioning

confidence: 99%

Cost Effective Analysis on Mathematical Modelling of HIV/AIDS with Optimal Control Strategy

Gurmu

Bole²,

Koya³

2022

ARJOM

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In this paper, a deterministic model of the Human Immunodeficiency Virus has been formulated to describe the transmission dynamics of the disease. The good posedness of the model equations was proved and the equilibrium points of the model have been identified. Basic reproduction numbers were used to establish both local and global stability of the disease-free and endemic equilibrium points of the model equation. The analysis reveals that if the basic reproduction is smaller than one, the solution converges to the disease-free steady-state, which is locally asymptotically stable. If the fundamental reproduction number is more than one, the solution converges to the endemic equilibrium point, which is locally asymptotically stable., sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of the Human Immunodeficiency Virus. The results of the simulation show that treatment minimizes the risk of Human Immunodeficiency Virus transmission from the community and the stability of disease-free equilibrium is achievable when basic reproduction is less. The findings from the analysis of cost-effectiveness revealed that a combination of prevention and screening is the most effective strategy to eradicate the disease from the community.

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“…Among the most popular are Ebola Virus [3], Hepatitis B Virus [4]. The Human Immunodeficiency Virus (HIV) [5][6][7]. These models have been helpful to study the control of the virus kinetics in order to provide a quantitative understanding and create public awareness of the virus, while [8][9][10][11][12][13] have designed mathematical models to explore the transmission dynamics and control of the infection.…”

Section: Introductionmentioning

confidence: 99%

Optimal control and effect of poor sanitation on modelling the acute diarrhea infection

Lasisi¹,

Akinwande²,

Abdulrahaman³

2020

J., complex., health sci.

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Acute diarrhea disease has a greater threat to human population especially in poor sanitary or hygienic environments, which caused enormous mortality and mobility in the Society. In this paper, we proposed a model to describe the transmission of the acute diarrhea disease and optimal control strategies in a community. The reproduction number and global dynamics of the model are obtained. Global Stability of the Disease free and endemic state of the model equations is determined. It was found that, the Disease Free Equilibrium is globally asymptotically stable in feasible region Ω if R0≤1 and Endemic state is globally asymptotically stable when R0>1. The Optimal control problem is designed with two control strategies, namely, the prevention through minimizing the contact between the infected with acute diarrhea infectious and susceptible, and treatment of an individual. The existence of optimal control model is obtained. Numerical results of the dynamics of the disease are presented. It was found that, as the effective contact rate increases, it increases the reproduction number of the model equations, also as the effectiveness of compliance of good hygiene increases, it decreases the reproduction number of the model by varying the contact rate and more so, as production rate of acute diarrhea bacteria increases, it increases the secondary cases of the infected individuals.

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Sensitivity Analysis of the Parameters of a Mathematical Model of Hepatitis B Virus Transmission

Cited by 10 publications

References 27 publications

The Continuous and Discrete Stability Characterization of Hepatitis B Deterministic Model

The Continuous and Discrete Stability Characterization of Hepatitis B Deterministic Model

Cost Effective Analysis on Mathematical Modelling of HIV/AIDS with Optimal Control Strategy

Optimal control and effect of poor sanitation on modelling the acute diarrhea infection

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