So Much to Model
So Little Time
Facing the Challenge
of Infectious Disease in Africa
Alex Welte
Computational and Applied Mathematics, Wits
Outline
Modeling Populations / Individuals / Assays
Purpose
Content
Limitations
Development
What To Do
Making Useful Models / Tools
Mine Existing Data
Influence Prospective Data
Communication / Collaborators
K103
V106
Incidence from Prevalence Surveys
1200 Antibody negative samples
Npositive
100
Strategy 1
10
2
mean
stdev
51.155
2.979
45.544
1.972
51.882
0.839
55.664
0.983
57.612
1.225
67.896
0.807
4
mean
stdev
86.879
6.679
77.431
4.432
73.254
1.989
76.733
2.331
80.437
2.857
87.339
2.003
6
mean
stdev
119.779
9.414
107.787
6.568
94.193
3.044
97.366
3.317
102.495
4.313
106.231
3.154
8
mean
stdev
150.306
11.511
136.817
8.340
114.549
4.194
117.318
4.529
123.912
5.508
124.814
4.193
10
mean
stdev
178.865
12.924
164.670
10.100
134.511
5.203
136.906
5.511
144.709
6.804
143.077
5.067
12
mean
stdev
205.355
14.162
191.055
11.622
154.133
5.966
156.174
6.465
164.756
7.967
160.700
6.108
14
mean
stdev
230.200
15.055
216.736
12.897
173.335
6.818
174.928
7.362
184.209
8.959
178.074
6.991
16
mean
stdev
253.931
15.483
241.057
13.962
192.023
7.724
193.487
8.077
203.266
9.858
195.104
7.616
18
mean
stdev
276.407
15.890
264.719
14.996
210.281
8.509
211.808
8.975
221.727
10.705
211.579
8.460
20
mean
stdev
297.978
16.417
287.522
16.074
228.458
9.152
229.598
9.963
239.522
11.481
228.109
9.118
1
100
Strategy 2
50
10
1
40
Strategy 3
20
10
5
1
36
Strategy 4
12
6
1
36
Strategy 5
6
1
25
Strategy 6
5
1
Trial Duration (years)
5
Risk group occupations
(fractions)
(at beginning of trial)
Pregnancy hazard
(fraction per year)
Infection hazard
(fraction per year)
Arm 1 ( effective gel)
Low risk group
High risk group
tot
0.3
0.7
1
0.01
0.02
0.017
0.0025
0.025
0.01825
Arm 2 ( placebo gel)
Low risk group
High risk group
tot
0.3
0.7
1
0.05
0.1
0.085
0.005
0.05
0.0365
1
0.2
0.5
Arm 2 / Arm 2
Fill in coloured cells
white cells generated
Assumptions
gel is (incidentally) a contraceptive
Fill in coloured cells
white cells generated
from assumed
effectiveness below
Fill in coloured cells
White cells calculated
from assumed
effectiveness below
risk distribution same
for both arms
Reduction factors
low risk
Reduction factors
Low risk
0.2
infection and pregnancy
occur independantly
high risk
inf hazard independent
of pregnancy
average Pregnancy
hazard reduction
ratio
high risk
0.2
0.5
average infection
hazard reduction
ratio:
0.2
Usage
Fill in ONLY the values in coloured cells
on left of freeze pane line
(i.e. cols B-D)
0.5
0.5
Observed hazard ratio / Actual hazard ratio
1.080
To Do
Raw Lab Data Analysis
Clinical Interpretation of Lab Data
Cohort / Survey Data Analysis
Protocol Design
Intervention Design
Cell / Virus Population Models
Modeling Evolution
Separation of Scales Analysis
Professional Development
The End
Not In Sight
Laundry List
Incidence from Prevalence Surveys
Inferring ‘Window Period’ Duration
Acute Infection Cell/Virus Dynamics
Pooling Samples for Diagnostics, Surveys
Bias in a Microbicide Trial
Incidence from Prevalence Time Series
Transiently Detectable Virus Genotypes
Calibrating RTPCR Inferred Relative Gene Frequencies
Viable Cell/Virion Life Cycle Models
Dosing Regimen Impacts on Virus Ecology
Immune System Dynamics
Calibrating RTPCR Melt Curves
Datamining Sequencer Chromatograms