Optimal control of the mathematical viral dynamic model of different hepatitis B infected individuals with numerical simulation

2019 ◽  
Vol 33 (26) ◽  
pp. 1950310 ◽  
Author(s):  
Tahir Khan ◽  
Aly R. Seadawy ◽  
Gul Zaman ◽  
Abdullah Abdullah
Keyword(s):  
Hepatitis B ◽  
Causes Of Death ◽  
Horizontal Transmission ◽  
Optimization Theory ◽  
Control Policy ◽  
Control Program ◽  
Geometrical Approach ◽  
Viral Dynamics ◽  
B Virus ◽  
Disease Free

The viral infection of hepatitis B virus (HBV) is a dangerous problem for health around the globe and counted in the top leading causes of death. To explore the viral dynamics of this infection, an HBV epidemic model has been developed by dividing the infected compartment into three subclasses, acute, chronically infected and carrier individuals with both vertical as well as horizontal transmission. After formulating the model, we prove that the positive solution of the model exists. The next generation matrix approach has been used to investigate the threshold quantity known as basic reproduction number. The global stability conditions at endemic equilibria (EE) and disease-free equilibrium (DFE) are established by using the method of geometrical approach and Castillo-Chavez, respectively. We use the optimization theory and the three time-dependent control variables to establish the control program. By the help of this control policy, we reduce the number of susceptible, acute, chronically hepatitis B infected and carrier persons, while the numbers of recovered and vaccinated populations are maximized. Finally, numerical results will be found out for the support and feasibility of the analytical results.

Role of Horizontal Transmission in Hepatitis B Virus Spread among Household Contacts in North India

Intervirology ◽  
2008 ◽  
Vol 51 (1) ◽  
pp. 7-13 ◽  
Author(s):  
Swati Gupta ◽  
Richa Gupta ◽  
Y.K. Joshi ◽  
Sarman Singh
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Horizontal Transmission ◽  
North India ◽  
Virus Spread ◽  
Household Contacts ◽  
B Virus

scholarly journals Mathematical Modeling of Transmission Dynamics and Optimal Control of Vaccination and Treatment for Hepatitis B Virus

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Ali Vahidian Kamyad ◽  
Reza Akbari ◽  
Ali Akbar Heydari ◽  
Aghileh Heydari
Keyword(s):  
Optimal Control ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Public Health Problem ◽  
Hbv Infection ◽  
Optimal Control Strategy ◽  
B Virus ◽  
Existence And Stability ◽  
Steady State Solutions ◽  
Disease Free

Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection.

scholarly journals Epidemiological patterns of hepatitis B virus (HBV) in highly endemic areasr

1996 ◽  
Vol 117 (2) ◽  
pp. 313-325 ◽  
Author(s):  
W. J. Edmunds ◽  
G. F. Medley ◽  
D. J. Nokes ◽  
C. J. O'Callaghan ◽  
H. C. Whittle ◽  
...  
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
East Asia ◽  
Horizontal Transmission ◽  
Perinatal Transmission ◽  
Sub Saharan Africa ◽  
B Virus ◽  
Age Dependent ◽  
Endemic Areas ◽  
Sub Saharan

SummaryThis paper uses meta-analysis of published data and a deterministic mathematical model of hepatitis B virus (HBV) transmission to describe the patterns of HBV infection in high endemicity areas. We describe the association between the prevalence of carriers and a simple measure of the rate of infection, the age at which half the population have been infected (A50), and assess the contribution of horizontal and perinatal transmission to this association. We found that the two main hyper-endemic areas of sub-Saharan Africa and east Asia have similar prevalences of carriers and values of A50, and that there is a negative nonlinear relationship between A50 and the prevalence of carriers in high endemicity areas (Spearman's Rank, P = 0·0086). We quantified the risk of perinatal transmission and the age-dependent rate of infection to allow a comparison between the main hyper-endemic areas. East Asia was found to have higher prevalences of HBeAg positive mothers and a greater risk of perinatal transmission from HBeAg positive mothers than sub-Saharan Africa, though the differences were not statistically significant. However, the two areas have similar magnitudes and age-dependent rates of horizontal transmission. Results of a simple compartmental model suggest that similar rates of horizontal transmission are sufficient to generate the similar patterns between A50 and the prevalences of carriers. Interrupting horizontal transmission by mass immunization is expected to have a significant, nonlinear impact on the rate of acquisition of new carriers.

scholarly journals The analysis of hepatitis B virus (HBV) transmission using an epidemic model

2021 ◽  
Vol 2 (1) ◽  
pp. 70-79
Author(s):  
Tahir Khan ◽  
Rahman Ullah ◽  
Gul Zaman
Keyword(s):  
Hepatitis B ◽  
Sufficient Conditions ◽  
Reproductive Number ◽  
Model Formulation ◽  
Important Conclusion ◽  
Disease Propagation ◽  
B Virus ◽  
Disease Free ◽  
Endemic State

In this article, we propose an epidemic problem of hepatitis B with vaccination. So to do this, first we presents the model formulation and prove that the solutions are bounded and positive. We obtain the disease free equilibrium and calculate the basic reproduction number (R0). The reproductive number will be used to find the endemic state of the model. We discuss the qualitative analysis of the proposed problem and show that whenever, R0 < 1 then the disease free equilibrium is stable locally and globally. Moreover, whenever, R0 > 1, then the endemic state is asymptotically stable. We derive sufficient conditions for both the equilibria and its stabilities. Further more numerical simulation are carried out to illustrate the feasibility of the obtained results and verified that with actual data, we are in the position to put down the hepatitis B infection form the community. We also highlight the role of epidemic parameters in the disease propagation. Our numerical works verified the analytical results. Finally some important conclusion are given at the end of the article.

Horizontal Transmission of Hepatitis B Virus Infection to United States-Born Children of Hmong Refugees

PEDIATRICS ◽  
1992 ◽  
Vol 89 (2) ◽  
pp. 269-273
Author(s):  
Marjorie B. Hurie ◽  
Eric E. Mast ◽  
Jeffrey P. Davis
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Hepatitis B Surface Antigen ◽  
Horizontal Transmission ◽  
Vaccination Schedule ◽  
Hepatitis B Vaccine ◽  
Hbv Infection ◽  
Childhood Vaccination ◽  
B Virus ◽  
Household Members

There is evidence that hepatitis B virus (HBV) transmission continues among Southeast Asian refugees after resettlement. To determine the prevalence of HBV infection (hepatitis B surface antigen [HBsAg] positive or core antibody positive) and modes of transmission in Hmong refugee households in Wisconsin, results of serologic tests were reviewed for 429 US-born children not previously vaccinated with hepatitis B vaccine and 754 of their Asian-born household members. The prevalence of HBV infection was 14% (62/429) among all US-born children, 30% (21/69) among children whose mothers were HBsAg-positive, and 11% (41/360) among children whose mothers were HBsAg-negative. Among children whose mothers were HBsAg-negative, the prevalence of HBV infection increased with increasing age (χ2 test for trend = 5.6, P .02) and was related to the household presence of HBsAg-positive sibling(s) (relative risk 4.0; 95% confidence interval = 1.5, 9.3; P &lt; .001). Of the 62 infected children, 13 (21%) lived in households with no HBsAg-positive household members. US-born children of Hmong refugees apparently acquire HBV infection through both horizontal and perinatal transmission. These findings emphasize the importance of routinely integrating hepatitis B vaccine doses into the childhood vaccination schedule for all infants whose parents are from areas where HBV infection is highly endemic. In addition, the findings support the need for pediatricians to consider vaccinating older children (up to age 7 years) whose parents are from HBV-endemic areas.

scholarly journals Viral dynamics in hepatitis B virus infection.

1996 ◽  
Vol 93 (9) ◽  
pp. 4398-4402 ◽  
Author(s):  
M. A. Nowak ◽  
S. Bonhoeffer ◽  
A. M. Hill ◽  
R. Boehme ◽  
H. C. Thomas ◽  
...  
Keyword(s):  
Hepatitis B Virus ◽  
Virus Infection ◽  
Hepatitis B ◽  
Hepatitis B Virus Infection ◽  
Viral Dynamics ◽  
B Virus
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