Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids
Abstract
:1. Introduction
2. Analysis of the Model
2.1. Non-Negativity and Boundedness of Solutions
2.2. Steady States
3. Mathematical Analysis of the Optimal Control
3.1. The Optimization Problem
3.2. An Optimal Control Existence Result
- (C1)
- The set of the corresponding state variables and controls is nonempty.
- (C2)
- The set is closed and convex.
- (C3)
- The right hand side of the state system is bounded by a linear function in the state and control variables.
- (C4)
- The integrand of the objective functional is concave on .
- (C5)
- There exists an and two constants , such that the integrand of the objective functional satisfies
3.3. The Optimality System
4. Numerical Results
Algorithm 1: The forward-backward finite difference numerical scheme. |
|
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Danane, J.; Allali, K. Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids. High-Throughput 2018, 7, 35. https://doi.org/10.3390/ht7040035
Danane J, Allali K. Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids. High-Throughput. 2018; 7(4):35. https://doi.org/10.3390/ht7040035
Chicago/Turabian StyleDanane, Jaouad, and Karam Allali. 2018. "Mathematical Analysis and Treatment for a Delayed Hepatitis B Viral Infection Model with the Adaptive Immune Response and DNA-Containing Capsids" High-Throughput 7, no. 4: 35. https://doi.org/10.3390/ht7040035