scholarly journals The Optimal Control Strategy of Virus Transmission Based on Caputo-Fabrizio Order

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.

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.


2013 ◽  
Vol 9 (2) ◽  
pp. 87-94 ◽  

Abstract This paper proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the uninfected CD4+T cells and minimize the cost of drug, utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus(HIV). The optimal pair of control and trajectories of this nonlinear system with quadratic cost functional is obtained by Fourier series approximation. The method is based upon expanding time varying functions in the nonlinear system as their Fourier series, using the operational matrices for integration and product. The problem is reduced into a set of algebraic equations


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.


2021 ◽  
Vol 21 (S2) ◽  
Author(s):  
Shuo Yang ◽  
Ge Chen ◽  
Yueping Li ◽  
Guanhai Li ◽  
Yingfang Liang ◽  
...  

Abstract Background Although the expenses of liver cirrhosis are covered by a critical illness fund under the current health insurance program in China, the medical costs associated with hepatitis B virus (HBV) related diseases is not well addressed. In order to provide evidence to address the problem, we investigated the trend of direct medical costs and associated factors in patients with chronic HBV infection. Methods A retrospective cohort study of 65,175 outpatients and 12,649 inpatients was conducted using a hospital information system database for the period from 2008 to 2015. Generalized estimating equations (GEE) were applied to explore associations between annual direct medical costs and corresponding factors, meanwhile quantile regression models were used to evaluate the effect of treatment modes on different quantiles of annual direct medical costs stratified by medical insurances. Results The direct medical costs increased with time, but the proportion of antiviral costs decreased with CHB progression. Antiviral costs accounted 54.61% of total direct medical costs for outpatients, but only 6.17% for inpatients. Non-antiviral medicine costs (46.06%) and lab tests costs (23.63%) accounted for the majority of the cost for inpatients. The direct medical costs were positively associated with CHB progression and hospitalization days in inpatients. The direct medical costs were the highest in outpatients with medical insurance and in inpatients with free medical service, and treatment modes had different effects on the direct medical costs in patients with and without medical insurance. Conclusions CHB patients had a heavy economic burden in Guangzhou, China, which increased over time, which were influenced by payment mode and treatment mode.


Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.


Author(s):  
Ali Mohammad Mokhtari ◽  
Mohsen Barouni ◽  
Mohsen Moghadami ◽  
Jafar Hassanzadeh ◽  
Rebecca Susan Dewey ◽  
...  

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