macpan

Towards General Compartmental Modelling

Steve Walker

McMaster University

3/28/23

Take-Home

• Compartmental modelling R package
• Free and open source
• McMasterPandemic reboot
• Blazing Fast
• Team-produced

github.com/mac-theobio/McMasterPandemic – github.com/canmod/macpan2

Outline

• Background and History
• Examples
• Speed 🚀
• Interface

Background and History

COVID-19 Model

mac-theobio.github.io/covid-19

COVID-19 Vaccination Model

mac-theobio.github.io/covid-19

Forecasting

mac-theobio.github.io/forecasts/outputs/ON_accuracy.html

Calibration – Trajectory Matching

• Toy simulated data example
• “Observed” case reports – dots
• Model-predicted case reports – line
• Optimize transmission rate using maximum likelihood

Timeline

+-----------+------+-------------------------------------------------------+
| nickname  | year | description                                           |
+-----------+------+-------------------------------------------------------+
| macpan1   | 2020 | original covid models in R engine                     |
| macpan1.5 | 2021 | fast C++ engine and flexibility for VOC modelling     |
| macpan2   | 2023 | general architecture to implement the lessons learned |
+-----------+------+-------------------------------------------------------+

macpan1 = github.com/mac-theobio/McMasterPandemic/releases/tag/v0.0.20.1

macpan1.5 = github.com/mac-theobio/McMasterPandemic

macpan2 = github.com/canmod/macpan2

More Examples of Usage

Examples of Usage

• COVID-19 forecasts for agencies
  • Public Health Agency of Canada
  • Ontario Science Table
  • World Health Organization
    • South Africa – provincial and national level
    • Afro-Regional – 49 countries
  • Public Health Ontario

Examples of Usage

• COVID-19 models for small jurisdictions
  • Newfoundland – Amy Hurford
  • Yukon – Lisa Kanary

Examples of Usage

• Model structures
  • Macpan modelling group’s base model
  • Extensions of macpan – vaccination, VOC, and waste-water models
  • Metapopulation model of Newfoundland – 1000s of compartments
  • Endemic COVID-19 model
  • Monkeypox with two risk groups

Division of Labour (aside)

• Players
  • Public / Stakeholders
  • Public Health Officials
  • Modellers

Division of Labour (aside)

• Players
  • Public / Stakeholders
  • Public Health Officials
  • Modellers
  • Software Developers and Product Managers

Division of Labour (aside)

• Modelling is hard, even with great software
• Modellers should focus on biology and math

Division of Labour (aside)

• Software development is hard too
• Developers should focus on other things
  • Finding out what slows down modellers
  • Building tools that speeds them up

Example – fit to 5 data streams (PHO)

Example – fit to 5 data streams (PHO)

Example – endemic COVID-19

Example – endemic COVID-19

Example – waste-water

Edmonton

• Prepared for Ontario Science Table by Maya Earn
• Macpan base model with waste-water compartment
• Fit to multiple data streams

Example – waste-water

Ottawa

• Prepared for Ontario Science Table by Maya Earn
• Macpan base model with waste-water compartment
• Fit to multiple data streams

Lessons – modeller needs and wants

• Speed
• Functionality-rich
• Extensible
• Numerically stable
• Modular model building
• Version controlled models
• Biologically principled
• Statistically principled

canmod.github.io/macpan-book/index.html#vision-and-direction

Computational Speed

Need for Many Simulations

• Model fitting
• Each iteration of the optimizer requires one simulation

Need for Many Simulations

• Forecast confidence intervals
• Draw parameters from a distribution
• Run one simulation per draw

Need for Many Simulations

• Scenario exploration
• Establish status-quo forecasts
• One forecast requires n simulations
• Run n more simulations for each additional scenario

Need for Many Simulations

• Sensitivity analysis
• Are results sensitive to modelling choices?
• Run one simulation per sensitivity test

Computational Speed

• Rewrote engine in C++
• Seconds to hours
• Not days to weeks

Computational Speed

✅ 👍 😄 🥳 🚀

“It is insanely fast and definitely saves me hours everyday and allows me to explore more scenarios. I can do many more things I couldn’t do before due to computational limitations.”

Computational Speed

✅ 👍 😄 🥳 🚀

Early benchmark

+-----------------+--------------+
| Engine          | Run Time (s) |
+-----------------+--------------+
| Original R      |       1741.0 |
| Refactored C++  |          7.8 |
+-----------------+--------------+

Speedup: 224x

Interface

Interface Principles

• Another component of speed
• More difficult to solve than run-time speed
• Identifying best practices is harder than writing code
• If you cannot do it manually, you cannot automate it
• Different interfaces for different roles

Interface for macpan 1.5

• macpan1 had no interface for model definition
• macpan1.5 was the first attempt to expose model definitions to the user

canmod.github.io/macpan-book

Interface for macpan 1.5

state = c(S = 20000, I = 100, R = 0)
params = c(gamma = 0.06, beta = 0.15, N = sum(state))

canmod.github.io/macpan-book

Interface for macpan 1.5

state = c(S = 20000, I = 100, R = 0)
params = c(gamma = 0.06, beta = 0.15, N = sum(state))
sir_model = (
  flexmodel(
    params = params,
    state = state
  )
)

canmod.github.io/macpan-book

Interface for macpan 1.5

state = c(S = 20000, I = 100, R = 0)
params = c(gamma = 0.06, beta = 0.15, N = sum(state))
sir_model = (
  flexmodel(
    params = params,
    state = state,
    start_date = "2000-01-01",
    end_date = "2000-05-01"
  )
)

canmod.github.io/macpan-book

Interface for macpan 1.5

state = c(S = 20000, I = 100, R = 0)
params = c(gamma = 0.06, beta = 0.15, N = sum(state))
sir_model = (
  flexmodel(
    params = params,
    state = state,
    start_date = "2000-01-01",
    end_date = "2000-05-01"
  )  
  %>% add_rate("S", "I", ~ (1/N) * (beta) * (I))
  %>% add_rate("I", "R", ~ (gamma))
)

canmod.github.io/macpan-book

Interface for macpan 1.5

state = c(S = 20000, I = 100, R = 0)
params = c(gamma = 0.06, beta = 0.15, N = sum(state))
sir_model = (
  flexmodel(
    params = params,
    state = state,
    start_date = "2000-01-01",
    end_date = "2000-05-01"
  )  
  %>% add_rate("S", "I", ~ (1/N) * (beta) * (I))
  %>% add_rate("I", "R", ~ (gamma))
)

canmod.github.io/macpan-book

Interface for macpan 1.5

• Advantages
  • Modellers can make their own fast models
  • Easy to read and define simple models
• Lessons
  • Limited model definition flexibility/extensibility
  • No underlying data structure
  • Challenging to maintain in real pipelines
  • Difficult to experiment with new interface designs

Interface for macpan 2

Goals:

• Retain speed gains of macpan 1.5
• Address flexibility/extensibility
• Address pipeline maintenance issues
• Architecture expects ideas about interface to change

Model Readability

• Model definitions as directories of files
• File format human-readable and computer-consumable
• See the differences between two model versions
• Stay organized with a revision history

Model Definition Files

canmod.net/misc/model_definitions

Model Definition Files

• List of variables
• States, parameters, derived quantities
• Separate from numerical values

canmod.net/misc/model_definitions

Model Definition Files

• List of variables
• States, parameters, derived quantities
• Separate from numerical values
• Classify in different ways
• Useful for structured models

canmod.net/misc/model_definitions

Model Definition Files

canmod.net/misc/model_definitions

Model Definition Files

canmod.net/misc/model_definitions

Who Makes the Definition Files?

• Depends on the user’s role
• Build different interfaces
  • Point-and-click
  • Tidyverse-style
  • Model products
• For now – Steve makes the files while talking to modellers

canmod.net/misc/model_definitions

Readable Model Definitions

Readable Model Definitions

Model Definition Files – The Point

• Establish a standard specification
• Build different interfaces on top
• Interfaces can change as we learn
• Interfaces can be tailored

canmod.net/misc/model_definitions

Extensibility

• Easy-flexible trade-off
• Easier tools tend to be less flexible
• Better tools soften this trade-off
• Modellers value flexibility more
• Role-based interfaces

Extensible – model definition files

Extensible – model products

(in development)

Worden & Porco – pubmed.ncbi.nlm.nih.gov/28900467

Baez et al. – arxiv.org/abs/2205.08373

Flynn-Primrose et al. – in prep

Extensible – general model operations

(in development)

Extensible – general model operations

(in development)

Extensible – general model operations

(in development)

Extensible – general model operations

(in development)

Extensible – math expressions

Simple Birth Process

simple_sims(iteration_exprs = list(x ~ x + 0.01 * x)
  , time_steps = 10
  , x = 1
)$value

 [1] 1.000000 1.010000 1.020100 1.030301 1.040604 1.051010 1.061520 1.072135
 [9] 1.082857 1.093685 1.104622

canmod.net/misc/cpp_side

Extensible – math expressions

Fibonacci

s = simple_sims(iteration_exprs = list(x ~ A %*% x)
  , time_steps = 10
  , A = matrix(c(1, 1, 1, 0), 2, 2)
  , x = c(1, 0)
)
dplyr::filter(s, row == 0)$value

 [1]  1  1  2  3  5  8 13 21 34 55 89

canmod.net/misc/cpp_side

Extensible – edit model expressions

ExprList(
  before = list(),
  during = list(),
  after = list()
)

canmod.net/misc/cpp_side

Extensible – edit model expressions

ExprList(
  before = list(N ~ sum(state_vector)),
  during = list(),
  after = list()
)

canmod.net/misc/cpp_side

Extensible – edit model expressions

ExprList(
  before = list(N ~ sum(state_vector)),
  
  during = list(
    # force of infection
    flow_vector[foi_index] ~ beta * state_vector[I_index] / N
  ),
  
  after = list()
)

canmod.net/misc/cpp_side

Extensible – edit model expressions

ExprList(
  before = list(N ~ sum(state_vector)),
  
  during = list(
    
    # force of infection
    flow_vector[foi_index] ~ beta * state_vector[I_index] / N,
    
    # state-update expressions common to a large class of models
    flows ~ flow_vector * state_vector[from_index],
    incidence_vector ~ groupSums(flows, to_index, n_states),
    outflow_vector ~ groupSums(flows, from_index, n_states),
    state_vector ~ state_vector + incidence_vector - outflow_vector
  ),
  
  after = list()
)

canmod.net/misc/cpp_side

Extensible – C++ Level

engine_eval(~ log(1))

     [,1]
[1,]    0

canmod.net/misc/cpp_side

Extensible – C++ Level

engine_eval(~ sin(1))

Error in TMBSimulator(m) : 
The tmb_model object is malformed,
with the following explanation:
Error in get_indices(x_char[is_func], vec = names(valid_funcs), vec_type = "functions",  : 
  
the expression given by:
sin(1)

contained the following functions:
sin

 that were not found in the list of available functions:
+ - * / ^ exp log ( c matrix %*% sum rep rowSums colSums groupSums [ block t rbind_time rbind_lag cbind_time cbind_lag : seq convolution cbind rbind time_step assign unpack recycle clamp dpois dnbinom dnorm rpois rnbinom rnorm
Please see ?engine_functions for more information on the available functions.

Extensible – C++ Level

All standard trig and special math functions can be included just as easily.

Well documented underlying Eigen C++ library https://eigen.tuxfamily.org/dox.

Extensible – plug into tidyverse

Extensible – plug into tidyverse

              matrix time row col        value
1       state_vector    0   S     1.000000e+02
2       state_vector    0   E     1.000000e+00
3       state_vector    0   I     0.000000e+00
4       state_vector    0   R     0.000000e+00
5       state_vector    1   S     1.000000e+02
6       state_vector    1   E     9.000000e-01
7       state_vector    1   I     1.000000e-01
8       state_vector    1   R     0.000000e+00
9       state_vector    2   S     9.996040e+01
10      state_vector    2   E     8.496040e-01
11      state_vector    2   I     1.840000e-01
12      state_vector    2   R     6.000000e-03
13      state_vector    3   S     9.988755e+01
14      state_vector    3   E     8.374860e-01
15      state_vector    3   I     2.579204e-01
16      state_vector    3   R     1.704000e-02
17      state_vector    4   S     9.978552e+01
18      state_vector    4   E     8.557692e-01
19      state_vector    4   I     3.261938e-01
20      state_vector    4   R     3.251522e-02
21      state_vector    5   S     9.965661e+01
22      state_vector    5   E     8.991009e-01
23      state_vector    5   I     3.921991e-01
24      state_vector    5   R     5.208685e-02
25      state_vector    6   S     9.950182e+01
26      state_vector    6   E     9.639838e-01
27      state_vector    6   I     4.585772e-01
28      state_vector    6   R     7.561879e-02
29      state_vector    7   S     9.932111e+01
30      state_vector    7   E     1.048295e+00
31      state_vector    7   I     5.274610e-01
32      state_vector    7   R     1.031334e-01
33      state_vector    8   S     9.911363e+01
34      state_vector    8   E     1.150943e+00
35      state_vector    8   I     6.006428e-01
36      state_vector    8   R     1.347811e-01
37      state_vector    9   S     9.887786e+01
38      state_vector    9   E     1.271619e+00
39      state_vector    9   I     6.796986e-01
40      state_vector    9   R     1.708197e-01
41      state_vector   10   S     9.861170e+01
42      state_vector   10   E     1.410624e+00
43      state_vector   10   I     7.660785e-01
44      state_vector   10   R     2.116016e-01
45      state_vector   11   S     9.831251e+01
46      state_vector   11   E     1.568747e+00
47      state_vector   11   I     8.611762e-01
48      state_vector   11   R     2.575663e-01
49      state_vector   12   S     9.797721e+01
50      state_vector   12   E     1.747177e+00
51      state_vector   12   I     9.663803e-01
52      state_vector   12   R     3.092369e-01
53      state_vector   13   S     9.760222e+01
54      state_vector   13   E     1.947442e+00
55      state_vector   13   I     1.083115e+00
56      state_vector   13   R     3.672197e-01
57      state_vector   14   S     9.718355e+01
58      state_vector   14   E     2.171369e+00
59      state_vector   14   I     1.212872e+00
60      state_vector   14   R     4.322066e-01
61      state_vector   15   S     9.671674e+01
62      state_vector   15   E     2.421049e+00
63      state_vector   15   I     1.357237e+00
64      state_vector   15   R     5.049789e-01
65      state_vector   16   S     9.619686e+01
66      state_vector   16   E     2.698815e+00
67      state_vector   16   I     1.517908e+00
68      state_vector   16   R     5.864131e-01
69      state_vector   17   S     9.561857e+01
70      state_vector   17   E     3.007223e+00
71      state_vector   17   I     1.696715e+00
72      state_vector   17   R     6.774876e-01
73      state_vector   18   S     9.497605e+01
74      state_vector   18   E     3.349025e+00
75      state_vector   18   I     1.895634e+00
76      state_vector   18   R     7.792905e-01
77      state_vector   19   S     9.426302e+01
78      state_vector   19   E     3.727152e+00
79      state_vector   19   I     2.116799e+00
80      state_vector   19   R     8.930285e-01
81      state_vector   20   S     9.347278e+01
82      state_vector   20   E     4.144677e+00
83      state_vector   20   I     2.362506e+00
84      state_vector   20   R     1.020036e+00
85      state_vector   21   S     9.259821e+01
86      state_vector   21   E     4.604784e+00
87      state_vector   21   I     2.635223e+00
88      state_vector   21   R     1.161787e+00
89      state_vector   22   S     9.163180e+01
90      state_vector   22   E     5.110709e+00
91      state_vector   22   I     2.937588e+00
92      state_vector   22   R     1.319900e+00
93      state_vector   23   S     9.056576e+01
94      state_vector   23   E     5.665684e+00
95      state_vector   23   I     3.272404e+00
96      state_vector   23   R     1.496155e+00
97      state_vector   24   S     8.939202e+01
98      state_vector   24   E     6.272849e+00
99      state_vector   24   I     3.642628e+00
100     state_vector   24   R     1.692500e+00
101     state_vector   25   S     8.810243e+01
102     state_vector   25   E     6.935156e+00
103     state_vector   25   I     4.051355e+00
104     state_vector   25   R     1.911057e+00
105     state_vector   26   S     8.668883e+01
106     state_vector   26   E     7.655241e+00
107     state_vector   26   I     4.501789e+00
108     state_vector   26   R     2.154139e+00
109     state_vector   27   S     8.514327e+01
110     state_vector   27   E     8.435281e+00
111     state_vector   27   I     4.997206e+00
112     state_vector   27   R     2.424246e+00
113     state_vector   28   S     8.345820e+01
114     state_vector   28   E     9.276816e+00
115     state_vector   28   I     5.540902e+00
116     state_vector   28   R     2.724078e+00
117     state_vector   29   S     8.162678e+01
118     state_vector   29   E     1.018055e+01
119     state_vector   29   I     6.136129e+00
120     state_vector   29   R     3.056533e+00
121     state_vector   30   S     7.964313e+01
122     state_vector   30   E     1.114615e+01
123     state_vector   30   I     6.786017e+00
124     state_vector   30   R     3.424700e+00
125     state_vector   31   S     7.750270e+01
126     state_vector   31   E     1.217197e+01
127     state_vector   31   I     7.493471e+00
128     state_vector   31   R     3.831861e+00
129     state_vector   32   S     7.520264e+01
130     state_vector   32   E     1.325483e+01
131     state_vector   32   I     8.261060e+00
132     state_vector   32   R     4.281470e+00
133     state_vector   33   S     7.274223e+01
134     state_vector   33   E     1.438976e+01
135     state_vector   33   I     9.090880e+00
136     state_vector   33   R     4.777133e+00
137     state_vector   34   S     7.012326e+01
138     state_vector   34   E     1.556976e+01
139     state_vector   34   I     9.984403e+00
140     state_vector   34   R     5.322586e+00
141     state_vector   35   S     6.735043e+01
142     state_vector   35   E     1.678561e+01
143     state_vector   35   I     1.094231e+01
144     state_vector   35   R     5.921650e+00
145     state_vector   36   S     6.443174e+01
146     state_vector   36   E     1.802574e+01
147     state_vector   36   I     1.196434e+01
148     state_vector   36   R     6.578189e+00
149     state_vector   37   S     6.137874e+01
150     state_vector   37   E     1.927617e+01
151     state_vector   37   I     1.304905e+01
152     state_vector   37   R     7.296049e+00
153     state_vector   38   S     5.820672e+01
154     state_vector   38   E     2.052057e+01
155     state_vector   38   I     1.419372e+01
156     state_vector   38   R     8.078992e+00
157     state_vector   39   S     5.493476e+01
158     state_vector   39   E     2.174047e+01
159     state_vector   39   I     1.539416e+01
160     state_vector   39   R     8.930616e+00
161     state_vector   40   S     5.158555e+01
162     state_vector   40   E     2.291563e+01
163     state_vector   40   I     1.664455e+01
164     state_vector   40   R     9.854265e+00
165     state_vector   41   S     4.818508e+01
166     state_vector   41   E     2.402453e+01
167     state_vector   41   I     1.793744e+01
168     state_vector   41   R     1.085294e+01
169     state_vector   42   S     4.476205e+01
170     state_vector   42   E     2.504512e+01
171     state_vector   42   I     1.926365e+01
172     state_vector   42   R     1.192918e+01
173     state_vector   43   S     4.134707e+01
174     state_vector   43   E     2.595558e+01
175     state_vector   43   I     2.061234e+01
176     state_vector   43   R     1.308500e+01
177     state_vector   44   S     3.797179e+01
178     state_vector   44   E     2.673531e+01
179     state_vector   44   I     2.197116e+01
180     state_vector   44   R     1.432174e+01
181     state_vector   45   S     3.466769e+01
182     state_vector   45   E     2.736587e+01
183     state_vector   45   I     2.332642e+01
184     state_vector   45   R     1.564001e+01
185     state_vector   46   S     3.146502e+01
186     state_vector   46   E     2.783195e+01
187     state_vector   46   I     2.466342e+01
188     state_vector   46   R     1.703960e+01
189     state_vector   47   S     2.839162e+01
190     state_vector   47   E     2.812216e+01
191     state_vector   47   I     2.596681e+01
192     state_vector   47   R     1.851940e+01
193     state_vector   48   S     2.547186e+01
194     state_vector   48   E     2.822971e+01
195     state_vector   48   I     2.722102e+01
196     state_vector   48   R     2.007741e+01
197     state_vector   49   S     2.272584e+01
198     state_vector   49   E     2.815276e+01
199     state_vector   49   I     2.841073e+01
200     state_vector   49   R     2.171067e+01
201     state_vector   50   S     2.016878e+01
202     state_vector   50   E     2.789454e+01
203     state_vector   50   I     2.952136e+01
204     state_vector   50   R     2.341532e+01
205     state_vector   51   S     1.781072e+01
206     state_vector   51   E     2.746315e+01
207     state_vector   51   I     3.053954e+01
208     state_vector   51   R     2.518660e+01
209     state_vector   52   S     1.565654e+01
210     state_vector   52   E     2.687101e+01
211     state_vector   52   I     3.145348e+01
212     state_vector   52   R     2.701897e+01
213     state_vector   53   S     1.370623e+01
214     state_vector   53   E     2.613422e+01
215     state_vector   53   I     3.225337e+01
216     state_vector   53   R     2.890618e+01
217     state_vector   54   S     1.195545e+01
218     state_vector   54   E     2.527158e+01
219     state_vector   54   I     3.293159e+01
220     state_vector   54   R     3.084138e+01
221     state_vector   55   S     1.039619e+01
222     state_vector   55   E     2.430368e+01
223     state_vector   55   I     3.348285e+01
224     state_vector   55   R     3.281728e+01
225     state_vector   56   S     9.017602e+00
226     state_vector   56   E     2.325190e+01
227     state_vector   56   I     3.390425e+01
228     state_vector   56   R     3.482625e+01
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664 incidence_vector   64   R     2.004599e+00
665 incidence_vector   65   S     0.000000e+00
666 incidence_vector   65   E     3.688410e-01
667 incidence_vector   65   I     1.407391e+00
668 incidence_vector   65   R     1.975273e+00
669 incidence_vector   66   S     0.000000e+00
670 incidence_vector   66   E     3.152183e-01
671 incidence_vector   66   I     1.303536e+00
672 incidence_vector   66   R     1.941200e+00
673 incidence_vector   67   S     0.000000e+00
674 incidence_vector   67   E     2.694120e-01
675 incidence_vector   67   I     1.204704e+00
676 incidence_vector   67   R     1.902940e+00
677 incidence_vector   68   S     0.000000e+00
678 incidence_vector   68   E     2.303858e-01
679 incidence_vector   68   I     1.111175e+00
680 incidence_vector   68   R     1.861046e+00
681 incidence_vector   69   S     0.000000e+00
682 incidence_vector   69   E     1.971994e-01
683 incidence_vector   69   I     1.023096e+00
684 incidence_vector   69   R     1.816054e+00
685 incidence_vector   70   S     0.000000e+00
686 incidence_vector   70   E     1.690138e-01
687 incidence_vector   70   I     9.405062e-01
688 incidence_vector   70   R     1.768476e+00
689 incidence_vector   71   S     0.000000e+00
690 incidence_vector   71   E     1.450911e-01
691 incidence_vector   71   I     8.633570e-01
692 incidence_vector   71   R     1.718798e+00
693 incidence_vector   72   S     0.000000e+00
694 incidence_vector   72   E     1.247891e-01
695 incidence_vector   72   I     7.915304e-01
696 incidence_vector   72   R     1.667472e+00
697 incidence_vector   73   S     0.000000e+00
698 incidence_vector   73   E     1.075540e-01
699 incidence_vector   73   I     7.248562e-01
700 incidence_vector   73   R     1.614915e+00
701 incidence_vector   74   S     0.000000e+00
702 incidence_vector   74   E     9.291168e-02
703 incidence_vector   74   I     6.631260e-01
704 incidence_vector   74   R     1.561512e+00
705 incidence_vector   75   S     0.000000e+00
706 incidence_vector   75   E     8.045855e-02
707 incidence_vector   75   I     6.061046e-01
708 incidence_vector   75   R     1.507609e+00
709 incidence_vector   76   S     0.000000e+00
710 incidence_vector   76   E     6.985250e-02
711 incidence_vector   76   I     5.535400e-01
712 incidence_vector   76   R     1.453518e+00
713 incidence_vector   77   S     0.000000e+00
714 incidence_vector   77   E     6.080466e-02
715 incidence_vector   77   I     5.051712e-01
716 incidence_vector   77   R     1.399520e+00
717 incidence_vector   78   S     0.000000e+00
718 incidence_vector   78   E     5.307165e-02
719 incidence_vector   78   I     4.607346e-01
720 incidence_vector   78   R     1.345859e+00
721 incidence_vector   79   S     0.000000e+00
722 incidence_vector   79   E     4.644883e-02
723 incidence_vector   79   I     4.199683e-01
724 incidence_vector   79   R     1.292751e+00
725 incidence_vector   80   S     0.000000e+00
726 incidence_vector   80   E     4.076435e-02
727 incidence_vector   80   I     3.826163e-01
728 incidence_vector   80   R     1.240384e+00
729 incidence_vector   81   S     0.000000e+00
730 incidence_vector   81   E     3.587391e-02
731 incidence_vector   81   I     3.484311e-01
732 incidence_vector   81   R     1.188918e+00
733 incidence_vector   82   S     0.000000e+00
734 incidence_vector   82   E     3.165643e-02
735 incidence_vector   82   I     3.171754e-01
736 incidence_vector   82   R     1.138489e+00
737 incidence_vector   83   S     0.000000e+00
738 incidence_vector   83   E     2.801026e-02
739 incidence_vector   83   I     2.886235e-01
740 incidence_vector   83   R     1.089210e+00
741 incidence_vector   84   S     0.000000e+00
742 incidence_vector   84   E     2.485000e-02
743 incidence_vector   84   I     2.625622e-01
744 incidence_vector   84   R     1.041175e+00
745 incidence_vector   85   S     0.000000e+00
746 incidence_vector   85   E     2.210382e-02
747 incidence_vector   85   I     2.387910e-01
748 incidence_vector   85   R     9.944582e-01
749 incidence_vector   86   S     0.000000e+00
750 incidence_vector   86   E     1.971129e-02
751 incidence_vector   86   I     2.171223e-01
752 incidence_vector   86   R     9.491182e-01
753 incidence_vector   87   S     0.000000e+00
754 incidence_vector   87   E     1.762143e-02
755 incidence_vector   87   I     1.973812e-01
756 incidence_vector   87   R     9.051984e-01
757 incidence_vector   88   S     0.000000e+00
758 incidence_vector   88   E     1.579122e-02
759 incidence_vector   88   I     1.794052e-01
760 incidence_vector   88   R     8.627294e-01
761 incidence_vector   89   S     0.000000e+00
762 incidence_vector   89   E     1.418427e-02
763 incidence_vector   89   I     1.630438e-01
764 incidence_vector   89   R     8.217299e-01
765 incidence_vector   90   S     0.000000e+00
766 incidence_vector   90   E     1.276973e-02
767 incidence_vector   90   I     1.481578e-01
768 incidence_vector   90   R     7.822088e-01
769 incidence_vector   91   S     0.000000e+00
770 incidence_vector   91   E     1.152142e-02
771 incidence_vector   91   I     1.346190e-01
772 incidence_vector   91   R     7.441657e-01
773 incidence_vector   92   S     0.000000e+00
774 incidence_vector   92   E     1.041707e-02
775 incidence_vector   92   I     1.223093e-01
776 incidence_vector   92   R     7.075929e-01
777 incidence_vector   93   S     0.000000e+00
778 incidence_vector   93   E     9.437690e-03
779 incidence_vector   93   I     1.111200e-01
780 incidence_vector   93   R     6.724759e-01
781 incidence_vector   94   S     0.000000e+00
782 incidence_vector   94   E     8.567061e-03
783 incidence_vector   94   I     1.009518e-01
784 incidence_vector   94   R     6.387945e-01
785 incidence_vector   95   S     0.000000e+00
786 incidence_vector   95   E     7.791292e-03
787 incidence_vector   95   I     9.171334e-02
788 incidence_vector   95   R     6.065240e-01
789 incidence_vector   96   S     0.000000e+00
790 incidence_vector   96   E     7.098467e-03
791 incidence_vector   96   I     8.332113e-02
792 incidence_vector   96   R     5.756353e-01
793 incidence_vector   97   S     0.000000e+00
794 incidence_vector   97   E     6.478336e-03
795 incidence_vector   97   I     7.569887e-02
796 incidence_vector   97   R     5.460965e-01
797 incidence_vector   98   S     0.000000e+00
798 incidence_vector   98   E     5.922068e-03
799 incidence_vector   98   I     6.877681e-02
800 incidence_vector   98   R     5.178726e-01
801 incidence_vector   99   S     0.000000e+00
802 incidence_vector   99   E     5.422032e-03
803 incidence_vector   99   I     6.249134e-02
804 incidence_vector   99   R     4.909269e-01
805 incidence_vector  100   S     0.000000e+00
806 incidence_vector  100   E     4.971623e-03
807 incidence_vector  100   I     5.678441e-02
808 incidence_vector  100   R     4.652208e-01

Extensible – plug into stan/tmb

sir_tmb = tmb_fun(sir_macpan)

• tmb is a model fitting package
• stan is a Bayesian inference package
• Better confidence intervals
• Flexible inference
• No need to make stan model

canmod.github.io/macpan-book/tmb-engine.html

Extensible – plug into stan/tmb

sir_tmb = tmb_fun(sir_macpan)
sir_stan = tmbstan(sir_tmb, chains = 1)

• tmb is a model fitting package
• stan is a Bayesian inference package
• Better confidence intervals
• Flexible inference
• No need to make stan model

canmod.github.io/macpan-book/tmb-engine.html

Extensible – plug into stan/tmb

sir_tmb = tmb_fun(sir_macpan)
sir_stan = tmbstan(sir_tmb, chains = 1)
traceplot(sir_stan, ncol = 1)

• tmb is a model fitting package
• stan is a Bayesian inference package
• Better confidence intervals
• Flexible inference
• No need to make stan model

canmod.github.io/macpan-book/tmb-engine.html

Take-Home

• Compartmental modelling R package
• Free and open source
• McMasterPandemic reboot
• Blazing Fast
• Team-produced

github.com/mac-theobio/McMasterPandemic – github.com/canmod/macpan2

Take-Home

• Team-produced

github.com/mac-theobio/McMasterPandemic – github.com/canmod/macpan2

Contributions, Contributors, Community

• Original developers were real modellers (Ben Bolker, Jonathan Dushoff, David Earn, Mike Li, Irena Papst)
• Pipeline development for delivering PHAC, OMT, and PHO forecasts (Irena Papst, Mike Li)
• Sharcnet C++ expertise (Weiguang Guan)
• Current R development (Darren Flynn-Primrose)
• Gather requirements from public health modellers and academics (Amy Hurford, Lisa Kanary, Caroline Colijn, Zahra Mohammadi, Claude Nadeau, Philippe Berthiaume)
• Mathematical rigor (Jonathan Dushoff, Darren Flynn-Primrose)
• Workshop this summer (Irena Papst)

Thank You