Modeling and Control of Infectious Diseases in the Host: With MATLAB and R

Cover
Modeling and Control of
Infectious Diseases in the Host:

With Matlab and R
Copyright
Dedication
About the Author
Preface
Acknowledgments
Part 1: Theoretical Biology Principles
1 Introduction
	1.1 Modeling and Control of Infectious Diseases
	1.2 Basics of Immunology
	1.3 Basics of Virology
	1.4 Viral Mutation and Drug Resistance
2 Mathematical Modeling Principles
	2.1 Mathematical Modeling
	2.2 Mathematical Preliminaries
	2.3 Dynamical Systems
	2.4 Population Modeling
3 Model Parameter Estimation
	3.1 Parameter Fitting
	3.2 Experimental Data
	3.3 Cost Function
	3.4 Optimization Problem
		Running the Optimizing Toolbox
	3.5 Identifiability
	3.6 Bootstrapping Parameters
	3.7 Sources of Errors and Limitations
		Choices of Initial Conditions in Skew Parameter Estimates
		Measurement Error Impairs the Parameter Estimates
		Data Asynchrony Generates Overlooked Measurement Error
		Sparse and Scarce Data Aggravate the Parameter Estimates
		Performance by Different Parameter Estimation Algorithms
	3.8 Concluding Remarks
Part 2: Modeling Host Infectious Diseases
4 Modeling Influenza Virus Infection
	4.1 Influenza Infection
	4.2 Modeling Influenza Infection
	4.3 Influenza Infection Model With Immune Response
	4.4 Postinfluenza Susceptibility to Pneumococcal Coinfection
	4.5 Concluding Remarks
5 Modeling Ebola Virus Infection
	5.1 Ebola Infection
	5.2 In Vitro Ebola Virus Infection Model
	5.3 In Vivo Ebola Virus Infection and Vaccination
	5.4 Concluding Remarks
6 Modeling HIV Infection
	6.1 HIV Infection
	6.2 HIV Disease Progression
	6.3 How Does HIV Cause AIDS?
	6.4 Mathematical Modeling of HIV Infection
	6.5 The Three Stages in HIV Infection
	6.6 Concluding Remarks
7 HIV Evolution During Treatment
	7.1 Antiretroviral Drugs for HIV Infection
	7.2 Guidelines for HAART Treatment
	7.3 Including HAART in Mathematical Models
	7.4 Basic Viral Mutation Treatment Models
	7.5 Model With Reservoirs That Replicate Virus Frequently
	7.6 Mutation Model With Latent CD4+ T Reservoirs
	7.7 Concluding Remarks
Part 3: Advanced Topics in Control Theory
8 Optimal Therapy Scheduling
	8.1 Optimal Control Background
		Hamilton-Jacobi Theory
		Maximum Principle
	8.2 Positive Switched Linear Systems
	8.3 Optimal Control for Positive Switched Systems
	8.4 Optimal Control to Mitigate HIV Escape
		Invariant Subspaces
		Generalized Symmetry Case for Viral Mutation
		General Solution for a 4-Variant Model
	8.5 Restatement as an Optimization Problem
	8.6 Dynamic Programming for Positive Switched Systems
		Algorithm 1: Reverse Time Solution
		Algorithm 2: Box Constraint Algorithm
		Algorithm 3: Joint Forward/Backward Box Constraint Algorithm
		Numerical Results for Discrete-Time Optimal Control
			Computational Resources
	8.7 Concluding Remarks
9 Suboptimal Therapy Scheduling
	9.1 Control of Switched Systems
	9.2 Continuous-Time Guaranteed Cost Control
	9.3 Discrete-Time Guaranteed Cost Control
	9.4 Model Predictive Control
	9.5 Mitigating HIV Escape Simulations
	9.6 Concluding Remarks
10 PK/PD-based Impulsive Control
	10.1 Introduction
	10.2 Inverse Optimal Impulsive Control
	10.3 Tailoring Influenza Treatment
	10.4 Concluding Remarks
Bibliography
Index
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