scholarly journals Application and Optimal Control for an HBV Model with Vaccination and Treatment

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jing Zhang ◽  
Suxia Zhang
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Least Squares Method ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Optimal Theory ◽  
B Virus ◽  
The Stability ◽  
Hbv Model

In this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reproductive number R0. Using the least squares method, the model is applied to simulate yearly new infected cases of hepatitis B in China from 2004 to 2016. Moreover, optimal control problem with newborn vaccination and treatment appearing as functions of time is analyzed by classical optimal theory. The existence of the solution to optimality system is proved, and the simulations are conducted to show the results when optimal control or current intervention is used.

A Numerical Simulation on the Effect of Vaccination and Treatments for the Fractional Hepatitis B Model

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Haile Habenom ◽  
D. L. Suthar ◽  
D. Baleanu ◽  
S. D. Purohit
Keyword(s):  
Hepatitis B ◽  
Nonlinear Equations ◽  
Control Strategies ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
B Virus ◽  
The Stability ◽  
Hbv Model ◽  
Raphson Method ◽  
Jacobi Collocation Method

Abstract The aim of this paper is to develop a fractional order mathematical model for describing the spread of hepatitis B virus (HBV). We also provide a rigorous mathematical analysis of the stability of the disease-free equilibrium (DFE) and the endemic equilibrium of the system based on the basic reproduction number. Here, the infectious disease HBV model is described mathematically in a nonlinear system of differential equations in a caputo sense, and hence, Jacobi collocation method is used to reduce into a system of nonlinear equations. Finally, Newton Raphson method is used for the systems of nonlinear equations to arrive at an approximate solution and matlab 2018 has helped us to simulate the nature of each compartment and effects of the possible control strategies (i.e., vaccination and isolation).

scholarly journals Optimal Control of HIV/AIDS in the Workplace in the Presence of Careless Individuals

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Baba Seidu ◽  
Oluwole D. Makinde
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Strategies ◽  
Nonlinear Dynamical System ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Nonlinear Dynamical ◽  
Basic Model ◽  
Hiv Aids

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number,R0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated whenR0<1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin’s Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

scholarly journals Analysis of a HBV Model with Diffusion and Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Noé Chan Chí ◽  
Eric ÁvilaVales ◽  
Gerardo García Almeida
Keyword(s):  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Spatial Diffusion ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
B Virus ◽  
Comparison Arguments ◽  
Hbv Model ◽  
Iteration Technique

This paper discussed a hepatitis B virus infection with delay, spatial diffusion, and standard incidence function. The local stability of equilibrium is obtained via characteristic equations. By using comparison arguments, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. If the basic reproductive number is greater than unity, by means of an iteration technique, sufficiently conditions are obtained for the global asymptotic stability of the infected steady state. Numerical simulations are carried out to illustrate our findings.

AN HBV MODEL WITH DIFFUSION AND AGE OF INFECTION

2010 ◽  
Vol 03 (04) ◽  
pp. 731-739
Author(s):  
Junyuan Yang ◽  
Fu Zheng ◽  
Xiaoyan Wang ◽  
Xuezhi Li
Keyword(s):  
Steady State ◽  
Hepatitis B Virus ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Spatial Diffusion ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
B Virus ◽  
Age Of Infection ◽  
Hbv Model

In this paper, a hepatitis B virus (HBV) model with spatial diffusion and age of infection is investigated. By analyzing the corresponding characteristic equations, the local stabilities of an infected steady state and an uninfected steady state are discussed. Furthermore, it is proved that if the basic reproductive number is less than unity, the uninfected steady state is globally asymptotically stable. Numerical simulations are carried out to illustrate the main results.

scholarly journals Optimal Control and Cost Effectiveness Analysis of SIRS Malaria Disease Model with Temperature Variability Factor

2021 ◽  
Vol 53 (1) ◽  
pp. 134-163
Author(s):  
Temesgen Duressa Keno ◽  
Oluwole Daniel Makinde ◽  
Legesse Lemecha Obsu
Keyword(s):  
Optimal Control ◽  
Cost Effectiveness ◽  
Initial Conditions ◽  
Control Strategies ◽  
Disease Model ◽  
Temperature Variability ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Bed Nets ◽  
Reproductive Number

In this study, we proposed and analyzed the optimal control and cost-effectiveness strategies for malaria epidemics model with impact of temperature variability. Temperature variability strongly determines the transmission of malaria. Firstly, we proved that all solutions of the model are positive and bounded within a certain set with initial conditions. Using the next-generation matrix method, the basic reproductive number at the present malaria-free equilibrium point was computed. The local stability and global stability of the malaria-free equilibrium were depicted applying the Jacobian matrix and Lyapunov function respectively when the basic reproductive number is smaller than one. However, the positive endemic equilibrium occurs when the basic reproductive number is greater than unity. A sensitivity analysis of the parameters was conducted; the model showed forward and backward bifurcation. Secondly, using Pontryagin’s maximum principle, optimal control interventions for malaria disease reduction are described involving three control measures, namely use of insecticide-treated bed nets, treatment of infected humans using anti-malarial drugs, and indoor residual insecticide spraying. An analysis of cost-effectiveness was also conducted. Finally, based on the simulation of different control strategies, the combination of treatment of infected humans and insecticide spraying was proved to be the most efficient and least costly strategy to eradicate the disease.

scholarly journals Stability Analysis and Cauchy Matrix of a Mathematical Model of Hepatitis B Virus with Control on Immune System near Neighborhood of Equilibrium Free Point

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 166
Author(s):  
Irina Volinsky ◽  
Salvo Danilo Lombardo ◽  
Paz Cheredman
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Interleukin 2 ◽  
Integral Form ◽  
Cauchy Matrix ◽  
Symmetry Properties ◽  
B Virus ◽  
The Stability ◽  
Hbv Model

Mathematical models are useful tools to describe the dynamics of infection and predict the role of possible drug combinations. In this paper, we present an analysis of a hepatitis B virus (HBV) model including cytotoxic T lymphocytes (CTL) and antibody responses, under distributed feedback control, expressed as an integral form to predict the effect of a combination treatment with interleukin-2 (IL-2). The method presented in this paper is based on the symmetry properties of Cauchy matrices C(t,s), which allow us to construct and analyze the stability of corresponding integro-differential systems.

scholarly journals Mathematical analysis of hepatitis B epidemic model with optimal control

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Inam Zada ◽  
Muhammad Naeem Jan ◽  
Nigar Ali ◽  
Dalal Alrowail ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Optimal Control ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Optimal Combination ◽  
Optimal Control Strategy ◽  
Education Campaign ◽  
B Virus ◽  
The Stability ◽  
Disease Free ◽  
Global Health Problem

AbstractInfection of hepatitis B virus (HBV) is a global health problem. We provide the study about hepatitis B virus dynamics that can be controlled by education campaign (awareness), vaccination, and treatment. Initially we bring constant controls in considerations for treatment, vaccination, and education campaign (awareness). In the case of constant controls, we study the stability and existence of the disease-free and endemic equilibria model’s solutions. Afterwards, we take time as a control and formulate the suitable optimal control problem, acquire optimal control strategy in order to reduce the number of humans that are infected and the costs associated. At the end, results of numerical simulations show that the optimal combination of education campaign (awareness), treatment, and vaccination is the most efficient way to control the infection of hepatitis B virus (HBV) infection.

scholarly journals Modeling Optimal Control of Cholera Disease Under the Interventions of Vaccination, Treatment and Education Awareness

2018 ◽  
Vol 10 (5) ◽  
pp. 137
Author(s):  
Hellen Namawejje ◽  
Emmanuel Obuya ◽  
Livingstone S. Luboobi
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Care Service ◽  
Equilibrium Points ◽  
Health Care Service ◽  
Medical Science ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Education Campaigns ◽  
Global Threat

Cholera is virulent disease that affects both children and adults and can kill within hours. It has long been, and continues to be, a global threat to public health regardless of the advancement of medical science and health care service available. In this paper we formulate and analyze a mathematical model of the dynamics and optimal con- trol strategies for cholera epidemic. We present and analyze a cholera model with controls: u1 for vaccination of the human population, u2 for treatment and u3 for health education campaigns. The basic reproductive number R0; the effective reproductive number Re; as well as disease free equilibrium and endemic equilibrium points are derived. We establish the conditions for optimal control of the cholera disease using the Pontryagin&#39;s maximum principle and simulate the model for different control strategies. The results show that vaccination and education campaigns should be applied from start of the epidemic in any community faced with cholera disease.

scholarly journals Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Oluwole Daniel Makinde ◽  
David Malonza
Keyword(s):  
Optimal Control ◽  
Typhoid Fever ◽  
Control Strategies ◽  
Cost Effective ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Effective Strategies ◽  
Next Generation Matrix ◽  
The Cost ◽  
Disease Free

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

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