Mathematics for Life Sciences and Medicine - Takeuchi Iwasa and Sato

226 Index

evolutionary change 162 exponential

delay 197 kernel 197

fatality 37
force	75
force of infection						155, 169
global stability					166
graphical representation 161
helper T cell				167
hepatitis B virus						155
hepatitis C virus						155
heterogeneity				91
Hopf bifurcation						62, 194
host	123–126, 128, 129, 132, 133,
139, 145
human immunodeficiency virus
(HIV)			155
immigration				36, 68, 76
immune cell				168
immune impairment 162, 167, 170
immune response						156, 157
immune selection						169
immunity		9, 20
adaptive		177
cross-immunity						124, 125, 127, 146
innate		177
immunotherapy					218
impairment of immune
response				157
impulses		29
incidence		12, 15, 17, 19, 24, 39, 40, 79,
82, 128, 131, 146
mass action				132, 138, 142, 144,
146, 147
standard			124, 132, 139, 140, 142,
144, 146, 147
infection		5, 11, 33, 78
infection rate				157
infective		8, 69
infectivity		31, 33, 39
input	10
integral equation						98, 118
invade	74
invariant principle						56

invasibility 159
invasion	162
isoclines	210
Jury 81, 85
Kendall model 98, 100, 101

Kermack–McKendrik model 98

kernels
exponential				180
uniform			180
Liapunov functionals 61
measures		18, 41, 42
metastasis			220
migration			34, 70, 76, 87
mixing		91
mobility		87, 89
mosquitoes			71, 72
movements			92
multi-patch			69, 91
o springs			26
outbreak		43
parasite		123–125, 129, 130
replication rate 137
strain		124, 138, 145, 146
patch	35, 68, 71, 73, 81, 83, 85, 88
pathogenicity				155–157
patients		38, 42
period	14
permanence			51, 58, 59, 64, 84
persistence			147
strong		145, 149
persistent
weakly		133
population			7, 23, 24, 89
positivity
solution			184
predator		34
prevalence			139, 141, 142, 144, 147
prevention			42
prey	34
probability			23, 39, 40
propagation			67
quarantine			18, 37, 40

R
maximization					129
R◦
maximization					146, 147
R◦	140
1
R0
maximization					124
radius		83, 90
recovery			27
replacement ratio
basic		124, 125, 127, 128, 138,
	142, 146
maximal 124, 128, 135, 146
net		139–141, 144, 147
relative			127, 128, 130, 133, 137
reproduction				13, 17, 77, 79, 80, 90, 92
reproduction number 124, 127
residence			86, 88
risk	81
SEIR models				53
SEIRS models				53
selection			141, 142
functional				127, 134
semiflow			134, 137, 148
SI models			53
SIR model			51–53
SIRS model				53
SIS model			51, 53
sojourn		127, 133, 137
spread		20, 38, 80
stability			16, 19, 25, 51, 53, 70, 85
globally			55–57, 59, 63
local		190
locally			55, 56, 63
stages		29
strategy			36
structure			26, 28, 74, 77
susceptibility				32
switch

				Index	227
stability		191
system
delay di erential equation 199
equivalent			199
target cell dependence				167
threshold	13, 51, 58, 63, 84
time delay		51, 53, 54, 56
discrete	54
distributed			54, 56, 58
infinite	55
timing
immune		178
response		178
total force of infection				160, 162
trade o s	129
transmissibility
vertical	147
transmission			7, 10, 22, 28, 30, 72,
137, 145
horizontal		142, 146, 147
propagule		128, 146
vertical	131, 142, 143, 146
waterborne			128
traveling wave			98, 101, 108, 114,
117–119
treatment
continuous			215
periodic		218
vaccination		18, 19, 24, 31
vector-disease model				98, 109, 118
viral epitope			156
viral strain		168
virulence	124, 131, 145, 146
management			123, 129
virus 8
virus evolution			155

virus induced impairment 155