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 ◽  
...  

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.

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Ali Vahidian Kamyad ◽  
Reza Akbari ◽  
Ali Akbar Heydari ◽  
Aghileh Heydari

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.


Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ruiqing Shi ◽  
Ting Lu ◽  
Cuihong Wang

In this paper, a fractional-order model is constructed to describe the transmission of Hepatitis B Virus (HBV). Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of two equilibriums are obtained. Thirdly, the stability of equilibriums are analyzed. After that, some numerical simulations are performed to verify the theoretical prediction. Finally, a brief discussion is presented.


1999 ◽  
Vol 25 (6) ◽  
pp. 621-626
Author(s):  
RYO MATSUSHITA ◽  
MARIKO ASAHI ◽  
FUJIO ICHIMURA ◽  
TAKUMA HASHIMOTO ◽  
EIKI MATSUSHITA ◽  
...  

Author(s):  
Folahan S. Akinboro ◽  
T. O. Oluyo ◽  
O. O. Kehinde ◽  
S. Alao

The transmission dynamics of Hepatitis B Virus in a population with infective immigrant is presented with the inclusion of an optimal control strategy to curtail the spread of the virus. To understand the spread of this infection, we develop a mathematical model with control variables of migrant screening and public sensitization. The optimality system is characterized using Pontryagin’s maximum principle and solve numerically with an implicit finite difference method.  Result of the numerical simulation is presented to illustrate the feasibility of this control strategy. The analysis reveals that combination of both control variables could be the most fruitful way to reduce the incidence of Hepatitis B virus.


PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11207
Author(s):  
Pakkapon Rattanachaisit ◽  
Sirinporn Suksawatamnuay ◽  
Supachaya Sriphoosanaphan ◽  
Kessarin Thanapirom ◽  
Panarat Thaimai ◽  
...  

Background Hepatitis B virus (HBV) pregenomic RNA (pgRNA) has gained increasing attention owing to its role in replication of covalently closed circular DNA (cccDNA) in HBV. This marker has the potential to be used in clinical programs aimed to manage HBV infections. However, several reports on HBV pgRNA levels in clinical cases have conflicting results. RNA is easily degraded when exposed to heat and other environmental stressors. However, the stability of HBV pgRNA, during blood sample collection before the standard automated quantification, has never been estimated. This study aimed to demonstrate the effect of two different temperature conditions and storage durations on the stability of HBV pgRNA. Method Blood from forty patients with chronic hepatitis B infection, who also showed evidence of active HBV DNA replication, was collected and processed within 2 h of collection. Plasma from each patient was divided and stored at 4 °C and 25 °C (room temperature) for six different storage durations (0, 2, 6, 12, 24, and 48 h) and subsequently transferred to −80 °C for storage. The effect of multiple cycles of freezing and thawing of plasma at −20 °C or −80 °C was evaluated using samples from ten patients. Quantification of pgRNA from the samples was performed simultaneously, using the digital polymerase chain reaction (dPCR) method. The differences in pgRNA levels at baseline and each time point were compared using generalized estimating equation (GEE). A change greater than 0.5 log10 copies/mL of pgRNA is considered clinically significant. Statistical analyses were conducted using Stata 16.0. Results The mean HBV pgRNA level in the initially collected plasma samples was 5.58 log10copies/mL (ranging from 3.08 to 8.04 log10 copies/mL). The mean pgRNA levels in samples stored for different time periods compared with the initial reference sample (time 0) significantly decreased. The levels of pgRNA for 6, 12, 24, and 48 h of storage reduced by −0.05 log10 copies/mL (95% confidence interval (CI) −0.095 to −0.005, p = 0.03), −0.075 log10 copies/mL (95% CI [−0.12 to −0.03], p = 0.001), −0.084 log10 copies/mL (95% CI [−0.13 to −0.039], p =  < 0.001), and −0.120 log10 copies/mL (95% CI [−0.17 to −0.076], p =  < 0.001), respectively. However, these changes were below 0.5 log10 copies/mL and thus were not clinically significant. Compared with the samples stored at 4 °C, there were no significant differences in pgRNA levels in samples stored at 25 °C for any of the storage durations (−0.01 log10 copies/mL; 95% CI [−0.708 to 0.689], p = 0.98). No significant difference in the levels of pgRNA was observed in the plasma samples, following four freeze-thaw cycles at −20 °C and −80 °C. Conclusion The plasma HBV pgRNA level was stable at 4 °C and at room temperature for at least 48 h and under multiple freeze-thaw cycles. Our results suggest that pgRNA is stable during the process of blood collection, and therefore results of pgRNA quantification are reliable.


2021 ◽  
Vol 9 ◽  
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xue Yang ◽  
Zhen Wang

Hepatitis B virus (HBV) is a serious threat to human health as it can cause the chronic hepatitis B, and eventually liver cancer. It also has become one of the major threats to public health in the world. In this paper, considering the rationality of using standard incidence in Caputo-Fabrizio fractional order HBV infection model, we propose a model with standard incidence. The analysis of local stability about the equilibrium and the simulation of global stability are given. We also use the real data to estimate the parameters of this model. The simulation results can fit the data well. Moreover, we propose an optimal control model and give the optimal therapy strategy, which show that optimal therapy can reduce the cost and side effects while ensuring the therapeutic effect.


2020 ◽  
Vol 19 ◽  
pp. 103599
Author(s):  
Hussam Alrabaiah ◽  
Mohammad A. Safi ◽  
Mahmoud H. DarAssi ◽  
Bashir Al-Hdaibat ◽  
Saif Ullah ◽  
...  

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