Virus dynamics Mathematical principles of immunology and virology

by Nowak, Martin A.; May, Robert

• ISBN13: 9780198504177
• ISBN10: 0198504179
• Format: Paperback
• Copyright: 2001-01-25
• Publisher: Oxford University Press

Summary

We know, down to the tiniest details, the molecular structure of the human immunodeficiency virus (HIV). Yet despite this tremendous accomplishment, and despite other remarkable advances in our understanding of individual viruses and cells of the immune system, we still have no agreedunderstanding of the ultimate course and variability of the pathogenesis of AIDS. Gaps in our understanding like these impede our efforts towards developing effective therapies and preventive vaccines. Martin Nowak and Robert M May describe the emerging field of theoretical immunology in thisaccessible and well- written text. Using mathematical modelling techniques, the authors set out their ideas about how populations of viruses and populations of immune system cells may interact in various circumstances, and how infectious diseases spread within patients. They explain how thisapproach to understanding infectious diseases can reveal insights into the dynamics of viral and other infections, and the interactions between infectious agents and immune responses. The book is structured around the examples of HIV/AIDS and Hepatitis B virus, although the approaches describedwill be more widely applicable. The authors use mathematical tools to uncover the detailed dynamics of the infection and the effects of antiviral therapy. Models are developed to describe the emergence of drug resistance, and the dynamics of immune responses, viral evolution, and mutation. Thepractical implications of this work for optimisation of the design of therapy and vaccines are discussed. The book concludes with a glance towards the future of this fascinating, and potentially highly useful, field of study.

Table of Contents

Introduction: viruses, immunity, equations	1	(10)
Viruses	1	(2)
Immunity	3	(3)
B cells	3	(1)
T cells	4	(2)
Mathematical biology	6	(3)
Further reading	9	(1)
HIV	10	(6)
Discovery	10	(1)
Some basic facts about HIV	11	(2)
Treatment	13	(1)
Origins of HIV	14	(1)
Further reading	15	(1)
The basic model of virus dynamics	16	(11)
The model	17	(1)
Dynamics	18	(3)
Equilibrium	21	(1)
The primary phase of HIV and SIV infection	21	(5)
Estimating R0	24	(1)
Vaccination to reduce R0	25	(1)
Further reading	26	(1)
Anti-viral drug therapy	27	(17)
Theory	30	(6)
HIV: reverse transcriptase inhibitors	30	(2)
HIV: protease inhibitors	32	(2)
Rise of uninfected cells	34	(1)
Long-lived infected cells	34	(2)
Experiment	36	(7)
Short-term decay	36	(2)
CD4 cell increase	38	(1)
Long-lived infected cells	39	(1)
Virion turnover	40	(1)
Triple-drug therapy	41	(1)
Eradication	42	(1)
Further reading	43	(1)
Dynamics of hepatitis B virus	44	(8)
Theory	45	(1)
Experiment	46	(4)
Comparing HBV and HIV	50	(1)
Further reading	51	(1)
Dynamics of immune responses	52	(17)
A self-regulating CTL response	53	(3)
Persistent infection or clearance	55	(1)
Variation in CTL responsiveness leads to a negative correlation between virus load and the magnitude of the CTL response	56	(1)
Other self-regulating immune responses	56	(2)
A nonlinear CTL response: predator---prey dynamics	58	(3)
Virus load reduction	59	(1)
Variation in immune responsiveness	59	(2)
A linear immune response	61	(2)
Dynamic elimination	63	(1)
The simplest models of immune response dynamics	63	(3)
Variation in immune responsiveness	66	(1)
Experimental observations: HTLV-1 and HIV-1, 2	66	(1)
Further reading	67	(2)
How fast do immune responses eliminate infected cells?	69	(13)
The rate of CTL-mediated lysis in vitro	71	(3)
The dynamics of CTL-mediated lysis	74	(3)
Model 1	75	(1)
Model 2	76	(1)
Virus decay slopes	77	(3)
Comparing HIV and HBV	80	(1)
Further reading	81	(1)
What is a quasispecies?	82	(8)
More than atoms in our universe	83	(1)
Quasispecies live in sequence space	84	(1)
Quasispecies explore fitness landscapes	84	(1)
The mathematics of quasispecies	85	(1)
Error-thresholds	86	(1)
Some fancier quasispecies maths	87	(1)
Viral quasispecies	88	(1)
Antigenic escape and optimum mutation rate	89	(1)
Further reading	89	(1)
The frequency of resistant mutant virus before anti-viral therapy	90	(7)
Wild-type and mutant differ by 1-point mutation	91	(1)
Wild-type and mutant differ by 2-point mutations	92	(1)
Wild-type and mutant differ by n-point mutations	93	(2)
Some practical implications	95	(1)
Further reading	96	(1)
Emergence of drug resistance	97	(13)
The basic model	100	(1)
Emergence of resistance during drug treatment	101	(4)
Equilibrium properties	102	(1)
Total gain of CD4 cells and total reduction of virus load are independent of inhibition of sensitive virus	103	(2)
A stronger drug selects for faster emergence of resistance	105	(1)
The probability of producing a resistant mutant during therapy	105	(3)
Summary	108	(1)
Further reading	109	(1)
Timing the emergence of resistance	110	(13)
Theory	110	(6)
Observation	116	(5)
The probability of producing replication competent provirus	117	(4)
Summary	121	(1)
Further reading	121	(2)
Simple antigenic variation	123	(14)
The basic model of antigenic variation	125	(4)
Antigenic variation of HIV: diversity threshold	129	(4)
Three kinds of observed lentivirus infections	133	(3)
Further reading	136	(1)
Advanced antigenic variation	137	(12)
Immune response can select for or against antigenic diversity	138	(5)
Cross-sectional comparisons	142	(1)
Antigenic variation of HIV with different parameter values	143	(4)
Cross-sectional comparisons	146	(1)
Comparison with data	147	(1)
Further reading	148	(1)
Multiple epitopes	149	(33)
Experimental evidence	153	(2)
The simplest multiple epitope model	155	(2)
Different parameters for different mutants	157	(5)
What determines immunodominance?	161	(1)
Activated CTLs arise from inactivated precursors	162	(5)
The neutral case: all mutants have the same replication rates	163	(1)
The mutants have different replication rates	164	(3)
The limit of large η	167	(1)
The 2 x 1 case	167	(7)
η = 0	167	(2)
η > 0	169	(5)
The limit of large η	174	(1)
Cross-reactivity within the variants of a given epitope	174	(1)
Immunogenicity and intracellular competition	175	(2)
Immunotherapy	177	(2)
Summary	179	(2)
Further reading	181	(1)
Everything we know so far and beyond	182	(6)
The mechanism of HIV-1 disease progression	182	(4)
How to overcome HIV	186	(1)
A quantitative immunology and virology	187	(1)
Further reading	187	(1)
Appendix A: Dynamics of resistance in different types of infected cells	188	(8)
Appendix B: Analysis of multiple epitope dynamics	196	(13)
B.1 An invariant of motion	196	(1)
B.2 Local dynamics of a multiple epitope equation	197	(3)
B.3 The 2 x 2 system	200	(7)
B.3.1 η = 0	200	(2)
B.3.2 η > 0	202	(2)
B.3.3 The limit of large η	204	(3)
B.4 Intracellular competition between epitopes	207	(2)
References	209	(24)
Index	233