From 3ccaf2ff2875057fd792739b022575e289671de7 Mon Sep 17 00:00:00 2001 From: stevencarlislewalker Date: Mon, 13 Jan 2025 10:57:48 -0500 Subject: [PATCH 1/2] reports and docs --- DESCRIPTION | 2 +- R/formula_list_generators.R | 4 +- R/mp_tmb_model_spec.R | 7 +- R/tmb_model_editors.R | 27 ++- inst/starter_models/shiver/README.Rmd | 17 +- inst/starter_models/shiver/README.md | 181 ++++++++---------- .../shiver/figures/diagram-1.png | Bin 8040 -> 8532 bytes .../shiver/figures/mult_traj_fit-1.png | Bin 87705 -> 87925 bytes inst/starter_models/sir/README.md | 14 +- inst/starter_models/sir/figures/diagram-1.png | Bin 6772 -> 7169 bytes man/mp_tmb_insert_reports.Rd | 26 ++- man/mp_tmb_model_spec.Rd | 7 +- man/state_updates.Rd | 4 +- 13 files changed, 164 insertions(+), 125 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index 39c085aa8..9c486eb45 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,6 +1,6 @@ Package: macpan2 Title: Fast and Flexible Compartmental Modelling -Version: 1.13.0 +Version: 2.0.0 Authors@R: c( person("Steve Walker", email="swalk@mcmaster.ca", role=c("cre", "aut")), person("Weiguang Guan", role="aut"), diff --git a/R/formula_list_generators.R b/R/formula_list_generators.R index d364f79e9..6b2017936 100644 --- a/R/formula_list_generators.R +++ b/R/formula_list_generators.R @@ -348,8 +348,8 @@ MockChangeModel = function() { ##' @examples ##' sir = mp_tmb_library("starter_models", "sir", package = "macpan2") ##' sir -##' sir |> mp_euler() |> mp_expand() -##' sir |> mp_rk4() |> mp_expand() +##' sir |> mp_euler() |> mp_expand() +##' sir |> mp_rk4() |> mp_expand() ##' sir |> mp_euler_multinomial() |> mp_expand() ##' ##' @name state_updates diff --git a/R/mp_tmb_model_spec.R b/R/mp_tmb_model_spec.R index 31d69d1f3..ef74315e1 100644 --- a/R/mp_tmb_model_spec.R +++ b/R/mp_tmb_model_spec.R @@ -299,9 +299,10 @@ must_save_time_args = function(formulas) { #' being evaluated. For example, expressions that generate stochasticity should #' be listed in \code{sim_exprs} because TMB objective functions must be #' continuous. -#' @param state_update (experimental) Optional character vector for how to -#' update the state variables when it is relevant. Options include `"euler"`, -#' `"rk4"`, and `"euler_multinomial"`. +#' @param state_update Optional character vector for how to update the state +#' variables when it is relevant. Can be the name of any +#' \code{\link{state_updates}} function with the `mp_` prefix removed (e.g., +#' `"euler"`, `"rk4"`, and `"euler_multinomial"`). #' #' @examples #' spec = mp_tmb_model_spec( diff --git a/R/tmb_model_editors.R b/R/tmb_model_editors.R index 4683f02a9..7fc7fb918 100644 --- a/R/tmb_model_editors.R +++ b/R/tmb_model_editors.R @@ -197,13 +197,34 @@ mp_tmb_delete = function(model #' @param incidence_name Name of the incidence variable to be transformed. #' @param report_prob Value to use for the reporting probability; the #' proportion of cases that get reported. -#' @param mean_delay Mean of the Gamma distribution of reporting delay times. +#' @param mean_delay Mean of the Gamma distribution of reporting delay times +#' measured in time steps. For example, if the mean delay time in days is 14 +#' and each time step in the model corresponds to one week, then `mean_delay` +#' should be set to `2`. #' @param cv_delay Coefficient of variation of the Gamma distribution of -#' reporting delay times. +#' reporting delay times, with time measured in time steps (see more on this +#' in the description of the `mean_delay` argument immediately above). #' @param reports_name Name of the new reports variable. #' @param report_prob_name Name of the variable containing `report_prob`. #' @param mean_delay_name Name of the variable containing `mean_delay`. #' @param cv_delay_name Name of the variable containing `cv_delay`. +#' @examples +#' sir = mp_tmb_library("starter_models", "sir", package = "macpan2") +#' sir_delays = mp_tmb_insert_reports(sir +#' , incidence_name = "infection" +#' , report_prob = 0.1 +#' , mean_delay = 14 +#' , cv_delay = 0.25 +#' , reports_name = "reports" +#' ) +#' sir_delays |> mp_print_during() +#' (sir_delays +#' |> mp_simulator( +#' time_steps = 50L +#' , outputs = c("infection", "reports"), 50L) +#' |> mp_trajectory() +#' ) +#' #' @export mp_tmb_insert_reports = function(model , incidence_name @@ -229,7 +250,7 @@ mp_tmb_insert_reports = function(model kernel_length = qgamma(0.95, shape, scale = scale) |> ceiling() |> as.integer() expressions = c( - sprintf("%s ~ pgamma(1:%s, 1/(%s), %s * (%s^2))", map$dist, kernel_length + 1L, cv_delay_name, mean_delay_name, cv_delay_name) + sprintf("%s ~ pgamma(1:%s, 1/(%s^2), %s * (%s^2))", map$dist, kernel_length + 1L, cv_delay_name, mean_delay_name, cv_delay_name) , sprintf("%s ~ %s[1:%s] - %s[0:%s]", map$delta, map$dist, kernel_length, map$dist, kernel_length - 1L) , sprintf("%s ~ %s * %s / sum(%s)", map$kernel, report_prob_name, map$delta, map$delta) , sprintf("%s ~ convolution(%s, %s)", reports_name, incidence_name, map$kernel) diff --git a/inst/starter_models/shiver/README.Rmd b/inst/starter_models/shiver/README.Rmd index 547f5a2ea..fcfa67fb5 100644 --- a/inst/starter_models/shiver/README.Rmd +++ b/inst/starter_models/shiver/README.Rmd @@ -338,9 +338,9 @@ Now we update the specification to include these defaults. spec = mp_tmb_update(spec , default = list( N = N - , V = V0 - , I = I0 - , H = H0 + , V = 0 # V0 + , I = 1 # I0 + , H = 0 # H0 , a = a , b = a , alpha = alpha @@ -369,6 +369,7 @@ shiver_calibrator = mp_tmb_calibrator( # we also want to estimate initial E , par = c("beta_v","beta_s","E", "sigma", "gamma_h") , outputs = states + , time = mp_sim_bounds(-15, 90, "steps") ) # print to check shiver_calibrator @@ -658,8 +659,8 @@ prior_distributions = list( , logit_report_prob = mp_normal(qlogis(0.1), sd_par) , logit_p = mp_normal(qlogis(1/4), 4) , log_E_I_ratio = mp_normal(0, sd_par) - , log_I = mp_normal(log(I0), sd_state) - , log_H = mp_normal(log(H0), sd_state) + , log_I = mp_normal(log(1), sd_state) + , log_H = mp_normal(log(1), sd_state) , log_R = mp_normal(log(1), sd_state) ) @@ -669,6 +670,9 @@ dd = rbind(reported_hospitalizations, reported_cases) # calibrate shiver_calibrator = mp_tmb_calibrator( spec = (multi_traj_spec + |> mp_tmb_update( + #default = list(log_I = 0, log_H = 0, log_R = 0) + ) |> mp_hazard() ) # row bind both observed data @@ -684,6 +688,7 @@ shiver_calibrator = mp_tmb_calibrator( # a flexible model of time variation. , tv = mp_rbf("rbf_beta", 5, sparse_tol = 1e-8) , outputs = c(states, "reported_incidence", "beta") + , time = mp_sim_bounds(-30, 90, "steps") ) ``` @@ -713,7 +718,7 @@ Our prior for `sigma` is similar to the posterior, but `gamma_h` seems to have b , fill = "red" , alpha = 0.3 ) - + geom_point(data = dd, aes(time, value)) + + geom_point(data = mutate(dd, time = time + 30L), aes(time, value)) + facet_wrap(vars(matrix), scales = 'free') + theme_bw() ) diff --git a/inst/starter_models/shiver/README.md b/inst/starter_models/shiver/README.md index fb1157408..83348da08 100644 --- a/inst/starter_models/shiver/README.md +++ b/inst/starter_models/shiver/README.md @@ -2,37 +2,25 @@ SHIVER = SEIR + H + V ================ Jennifer Freeman, Steve Walker -- Packages Used and Settings -- Model - Specification -- States -- Parameters -- Variable Vaccination Rate -- Dynamics -- Calibration - Example - - Calibration Scenario - - Deciding - on Defaults - - Simulating - Dynamics - - Estimating Parameters - - Re-parameterizing - and Introducing Transformations - - Runge-Kutta 4 - - Fitting to Multiple - Trajectories - - Parameter Identifiability -- Model - Specification -- References +- [Packages Used and Settings](#packages-used-and-settings) +- [Model Specification](#model-specification) +- [States](#states) +- [Parameters](#parameters) +- [Variable Vaccination Rate](#variable-vaccination-rate) +- [Dynamics](#dynamics) +- [Calibration Example](#calibration-example) + - [Calibration Scenario](#calibration-scenario) + - [Deciding on Defaults](#deciding-on-defaults) + - [Simulating Dynamics](#simulating-dynamics) + - [Estimating Parameters](#estimating-parameters) + - [Re-parameterizing and Introducing + Transformations](#re-parameterizing-and-introducing-transformations) + - [Runge-Kutta 4](#runge-kutta-4) + - [Fitting to Multiple + Trajectories](#fitting-to-multiple-trajectories) + - [Parameter Identifiability](#parameter-identifiability) +- [Model Specification](#model-specification-1) +- [References](#references) This model builds on the basic SEIR model, with two additional compartments for vaccination and hospitalizations. @@ -115,22 +103,22 @@ article](https://github.com/canmod/macpan2/blob/main/inst/starter_models/shiver/ | E | Number of exposed individuals | | R | Number of recovered individuals | -The size of the total population is, $N = S + H + I + V + E + R$, and +The size of the total population is, $N = S + H + I + V + E + R$, and the disease spreads through homogeneous mixing of the subpopulation $N_{\text{mix}}=N -H$. # Parameters -| variable | description | -|------------|-----------------------------------------------------------------------------------------------------| -| $\phi$ | per capita vaccination rate of susceptibles | -| $\rho$ | per capita vaccine waning rate | -| $\beta_S$ | per capita transmission rate for susceptibles (in $N_{\text{mix}}$ population) | -| $\beta_V$ | per capita transmission rate for vaccinated individuals (in $N_{\text{mix}}$ population) | -| $\alpha$ | per capita infection rate (average time spent in compartment $E$ is $1/\alpha$) | -| $\gamma_I$ | per capita recovery rate for infected individuals | -| $\gamma_H$ | per capita recovery rate for hospitalized individuals | -| $\sigma$ | per capita rate at which infected individuals develop severe infections and require hospitalization | +| variable | description | +|----|----| +| $\phi$ | per capita vaccination rate of susceptibles | +| $\rho$ | per capita vaccine waning rate | +| $\beta_S$ | per capita transmission rate for susceptibles (in $N_{\text{mix}}$ population) | +| $\beta_V$ | per capita transmission rate for vaccinated individuals (in $N_{\text{mix}}$ population) | +| $\alpha$ | per capita infection rate (average time spent in compartment $E$ is $1/\alpha$) | +| $\gamma_I$ | per capita recovery rate for infected individuals | +| $\gamma_H$ | per capita recovery rate for hospitalized individuals | +| $\sigma$ | per capita rate at which infected individuals develop severe infections and require hospitalization | # Variable Vaccination Rate @@ -629,25 +617,25 @@ print(reparameterized_spec) #> --------------------- #> Default values: #> --------------------- -#> matrix row col value -#> a 1.684889e+04 -#> b 1.684889e+04 -#> rho 5.555556e-03 -#> beta_s 2.000000e-01 -#> beta_v 5.000000e-02 -#> alpha 3.030303e-01 -#> gamma_i 1.000000e-01 -#> gamma_h 7.000000e-02 -#> sigma 1.000000e-01 -#> N 1.480000e+08 -#> I 2.718571e+03 -#> V 1.015657e+04 -#> E 0.000000e+00 -#> H 6.300000e+01 -#> R 0.000000e+00 -#> logit_p -4.595120e+00 -#> log_beta -4.605170e+00 -#> log_E_I_ratio -4.605170e+00 +#> quantity value +#> a 1.684889e+04 +#> b 1.684889e+04 +#> rho 5.555556e-03 +#> beta_s 2.000000e-01 +#> beta_v 5.000000e-02 +#> alpha 3.030303e-01 +#> gamma_i 1.000000e-01 +#> gamma_h 7.000000e-02 +#> sigma 1.000000e-01 +#> N 1.480000e+08 +#> I 2.718571e+03 +#> V 1.015657e+04 +#> E 0.000000e+00 +#> H 6.300000e+01 +#> R 0.000000e+00 +#> logit_p -4.595120e+00 +#> log_beta -4.605170e+00 +#> log_E_I_ratio -4.605170e+00 #> #> --------------------- #> Before the simulation loop (t = 0): @@ -922,45 +910,45 @@ shiver_calibrator = mp_tmb_calibrator( Next we optimize, and look at our estimates. - #> mat row default estimate std.error - #> 1 time_var_rbf_beta 1 0.0000 -0.0300 0.0487 - #> 2 time_var_rbf_beta 2 0.0000 0.0485 0.0541 - #> 3 time_var_rbf_beta 3 0.0000 -0.0695 0.0679 - #> 4 time_var_rbf_beta 4 0.0000 0.1091 0.0907 - #> 5 prior_sd_rbf_beta 0 1.0000 0.5297 0.0177 - #> 6 distr_params_sd_H 0 1.0000 0.0752 0.0157 - #> 7 distr_params_sd_reported_incidence 0 1.0000 0.2209 0.0187 - #> 8 time_var_rbf_beta 0 0.0000 -0.0270 0.0431 - #> 9 beta 0 0.0100 0.3099 0.0443 - #> 10 sigma 0 0.0498 0.0336 0.0113 - #> 11 gamma_h 0 0.0498 0.9811 0.1856 - #> 12 E_I_ratio 0 0.0100 0.0851 0.1017 - #> 13 I 0 2718.5714 2986.9423 943.6758 - #> 14 H 0 63.0000 0.1453 2.9807 - #> 15 R 0 1.0000 1.0000 54.5981 - #> 16 report_prob 0 0.5000 0.8292 0.2194 - #> 17 p 0 0.0100 0.2197 9.1710 + #> mat row default estimate std.error + #> 1 time_var_rbf_beta 1 0.0000 0.2706 NaN + #> 2 time_var_rbf_beta 2 0.0000 -0.0580 0.1147 + #> 3 time_var_rbf_beta 3 0.0000 -0.0752 0.3265 + #> 4 time_var_rbf_beta 4 0.0000 0.0829 0.8638 + #> 5 prior_sd_rbf_beta 0 1.0000 0.5297 0.0177 + #> 6 distr_params_sd_H 0 1.0000 0.0732 0.0051 + #> 7 distr_params_sd_reported_incidence 0 1.0000 1.8991 0.1423 + #> 8 time_var_rbf_beta 0 0.0000 -0.4327 NaN + #> 9 beta 0 0.0100 0.8061 0.2597 + #> 10 sigma 0 0.0498 0.0004 0.0003 + #> 11 gamma_h 0 0.0498 0.0233 0.0022 + #> 12 E_I_ratio 0 0.0100 0.0839 0.1239 + #> 13 I 0 2718.5714 28127.2583 22697.4586 + #> 14 H 0 63.0000 97.0439 7.5258 + #> 15 R 0 1.0000 1.0000 54.5978 + #> 16 report_prob 0 0.5000 0.5631 0.4171 + #> 17 p 0 0.0100 0.2405 9.8432 #> conf.low conf.high - #> 1 -0.1255 6.550000e-02 - #> 2 -0.0576 1.546000e-01 - #> 3 -0.2026 6.360000e-02 - #> 4 -0.0687 2.869000e-01 + #> 1 NaN NaN + #> 2 -0.2828 1.668000e-01 + #> 3 -0.7150 5.647000e-01 + #> 4 -1.6102 1.776000e+00 #> 5 0.4951 5.643000e-01 - #> 6 0.0445 1.060000e-01 - #> 7 0.1843 2.574000e-01 - #> 8 -0.1116 5.750000e-02 - #> 9 0.2342 4.102000e-01 - #> 10 0.0174 6.490000e-02 - #> 11 0.6772 1.421400e+00 - #> 12 0.0082 8.853000e-01 - #> 13 1608.0649 5.548174e+03 - #> 14 0.0000 4.193101e+16 - #> 15 0.0000 2.978526e+46 - #> 16 0.1891 9.902000e-01 + #> 6 0.0631 8.330000e-02 + #> 7 1.6201 2.178100e+00 + #> 8 NaN NaN + #> 9 0.4287 1.515700e+00 + #> 10 0.0001 1.600000e-03 + #> 11 0.0193 2.810000e-02 + #> 12 0.0046 1.518600e+00 + #> 13 5784.2259 1.367759e+05 + #> 14 83.3599 1.129742e+02 + #> 15 0.0000 2.978104e+46 + #> 16 0.0444 9.728000e-01 #> 17 0.0000 1.000000e+00 Our prior for `sigma` is similar to the posterior, but `gamma_h` seems -to have been pushed up by the data from about `0.05` to about 0.98. We +to have been pushed up by the data from about `0.05` to about 0.02. We still do not have confidence in our estimate of `p`. We now have five other parameters controlling transmission, and so to interpret them we really need a plot of how transmission varies over time in the model. We @@ -1092,7 +1080,8 @@ for details). # References -
+
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b/inst/starter_models/sir/README.md index 3b11aa7dd..7390eb6d1 100644 --- a/inst/starter_models/sir/README.md +++ b/inst/starter_models/sir/README.md @@ -150,12 +150,12 @@ print(spec |> mp_expand()) #> --------------------- #> Default values: #> --------------------- -#> matrix row col value -#> beta 0.2 -#> gamma 0.1 -#> N 100.0 -#> I 1.0 -#> R 0.0 +#> quantity value +#> beta 0.2 +#> gamma 0.1 +#> N 100.0 +#> I 1.0 +#> R 0.0 #> #> --------------------- #> Before the simulation loop (t = 0): @@ -165,7 +165,7 @@ print(spec |> mp_expand()) #> --------------------- #> At every iteration of the simulation loop (t = 1 to T): #> --------------------- -#> 1: infection ~ S * (I * beta/N) +#> 1: infection ~ S * (beta * I/N) #> 2: recovery ~ I * (gamma) #> 3: S ~ S - infection #> 4: I ~ I + infection - recovery diff --git a/inst/starter_models/sir/figures/diagram-1.png b/inst/starter_models/sir/figures/diagram-1.png index 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zhb*EjBr?CNr(M^b#Z$g)V);nno-ZZ~>)gt`fY}Wjf6iKHy8UEiX7ymhsJ^@e0zB;q zqA_)yejZ1keQ>+;L{rPUs;}G_4oNsepV?L{$%W&dL474V8?+lgUVCk*&I5g3{GMGR zaUDgqV0-;V(-^X2n7kq))2nz=Mf&LW6fiHYw~qpIKev(-f@{$z|BPR_ZXbS0we4)jU z!K@fM4vgdE+FeG7sEl=lsH0_Pn^O>!y!oJbP-Zu9f6wS0P2fJ#!QIgtQ;)KjTo z>xg$>M?a%qwy7Cc9qZZ%hMBrZdzKF-9BmLp>3DzfjpY)6OgabOJf#}&Jp^o`v*I67>Yk+L|&PM zIszK`{!I9h{A(Yy&i}Cr0y2UC;pQcONCjxd%nva5-%$R0EB|X+@h4G370$B1lJoP^ zCG(U|-EnmMP0#@T4@lyEz{tt-N2wCbB>i`Ew*N~Meqsd?lH6~rxWD}k*+4TSvN!mT zF#o>*;U`7-&IAHUqA`cCFO{2P}|=$`bjAN4+TS@Rr(q= VgWR|jLgKvuH5E mp_print_during() +(sir_delays + |> mp_simulator( + time_steps = 50L + , outputs = c("infection", "reports"), 50L) + |> mp_trajectory() +) + +} diff --git a/man/mp_tmb_model_spec.Rd b/man/mp_tmb_model_spec.Rd index d481e6bd8..e97896143 100644 --- a/man/mp_tmb_model_spec.Rd +++ b/man/mp_tmb_model_spec.Rd @@ -65,9 +65,10 @@ being evaluated. For example, expressions that generate stochasticity should be listed in \code{sim_exprs} because TMB objective functions must be continuous.} -\item{state_update}{(experimental) Optional character vector for how to -update the state variables when it is relevant. Options include \code{"euler"}, -\code{"rk4"}, and \code{"euler_multinomial"}.} +\item{state_update}{Optional character vector for how to update the state +variables when it is relevant. Can be the name of any +\code{\link{state_updates}} function with the \code{mp_} prefix removed (e.g., +\code{"euler"}, \code{"rk4"}, and \code{"euler_multinomial"}).} } \description{ Specify a simulation model in the TMB engine. diff --git a/man/state_updates.Rd b/man/state_updates.Rd index 47c9eb699..1e9189d05 100644 --- a/man/state_updates.Rd +++ b/man/state_updates.Rd @@ -86,8 +86,8 @@ distribution. \examples{ sir = mp_tmb_library("starter_models", "sir", package = "macpan2") sir -sir |> mp_euler() |> mp_expand() -sir |> mp_rk4() |> mp_expand() +sir |> mp_euler() |> mp_expand() +sir |> mp_rk4() |> mp_expand() sir |> mp_euler_multinomial() |> mp_expand() } From 66bcabea3df6bbed4dbb546bf94af6cc28225a4a Mon Sep 17 00:00:00 2001 From: stevencarlislewalker Date: Wed, 15 Jan 2025 10:25:42 -0500 Subject: [PATCH 2/2] revert shiver readme for now --- inst/starter_models/shiver/README.md | 185 ++++++++++++++------------- 1 file changed, 98 insertions(+), 87 deletions(-) diff --git a/inst/starter_models/shiver/README.md b/inst/starter_models/shiver/README.md index 83348da08..a237f5069 100644 --- a/inst/starter_models/shiver/README.md +++ b/inst/starter_models/shiver/README.md @@ -2,25 +2,37 @@ SHIVER = SEIR + H + V ================ Jennifer Freeman, Steve Walker -- [Packages Used and Settings](#packages-used-and-settings) -- [Model Specification](#model-specification) -- [States](#states) -- [Parameters](#parameters) -- [Variable Vaccination Rate](#variable-vaccination-rate) -- [Dynamics](#dynamics) -- [Calibration Example](#calibration-example) - - [Calibration Scenario](#calibration-scenario) - - [Deciding on Defaults](#deciding-on-defaults) - - [Simulating Dynamics](#simulating-dynamics) - - [Estimating Parameters](#estimating-parameters) - - [Re-parameterizing and Introducing - Transformations](#re-parameterizing-and-introducing-transformations) - - [Runge-Kutta 4](#runge-kutta-4) - - [Fitting to Multiple - Trajectories](#fitting-to-multiple-trajectories) - - [Parameter Identifiability](#parameter-identifiability) -- [Model Specification](#model-specification-1) -- [References](#references) +- Packages Used and Settings +- Model + Specification +- States +- Parameters +- Variable Vaccination Rate +- Dynamics +- Calibration + Example + - Calibration Scenario + - Deciding + on Defaults + - Simulating + Dynamics + - Estimating Parameters + - Re-parameterizing + and Introducing Transformations + - Runge-Kutta 4 + - Fitting to Multiple + Trajectories + - Parameter Identifiability +- Model + Specification +- References This model builds on the basic SEIR model, with two additional compartments for vaccination and hospitalizations. @@ -29,7 +41,7 @@ Vaccines are typically subject to resource constraints and distribution strategies might prioritize vaccinations for specific subpopulations, such as immunocompromised people, to reduce bad outcomes. We model this with a flow of susceptibles entering the vaccination class. This flow -could be a fixed rate, i.e. a constant proportion of the population +could be a fixed rate, i.e. a constant proportion of the population receives a vaccine each time step, but instead we wish to capture a more realistic vaccination rate by allowing it to vary (see [Variable Vaccination Rate](#variable-vaccination-rate)). @@ -103,22 +115,22 @@ article](https://github.com/canmod/macpan2/blob/main/inst/starter_models/shiver/ | E | Number of exposed individuals | | R | Number of recovered individuals | -The size of the total population is, $N = S + H + I + V + E + R$, and +The size of the total population is, $N = S + H + I + V + E + R$, and the disease spreads through homogeneous mixing of the subpopulation $N_{\text{mix}}=N -H$. # Parameters -| variable | description | -|----|----| -| $\phi$ | per capita vaccination rate of susceptibles | -| $\rho$ | per capita vaccine waning rate | -| $\beta_S$ | per capita transmission rate for susceptibles (in $N_{\text{mix}}$ population) | -| $\beta_V$ | per capita transmission rate for vaccinated individuals (in $N_{\text{mix}}$ population) | -| $\alpha$ | per capita infection rate (average time spent in compartment $E$ is $1/\alpha$) | -| $\gamma_I$ | per capita recovery rate for infected individuals | -| $\gamma_H$ | per capita recovery rate for hospitalized individuals | -| $\sigma$ | per capita rate at which infected individuals develop severe infections and require hospitalization | +| variable | description | +|------------|-----------------------------------------------------------------------------------------------------| +| $\phi$ | per capita vaccination rate of susceptibles | +| $\rho$ | per capita vaccine waning rate | +| $\beta_S$ | per capita transmission rate for susceptibles (in $N_{\text{mix}}$ population) | +| $\beta_V$ | per capita transmission rate for vaccinated individuals (in $N_{\text{mix}}$ population) | +| $\alpha$ | per capita infection rate (average time spent in compartment $E$ is $1/\alpha$) | +| $\gamma_I$ | per capita recovery rate for infected individuals | +| $\gamma_H$ | per capita recovery rate for hospitalized individuals | +| $\sigma$ | per capita rate at which infected individuals develop severe infections and require hospitalization | # Variable Vaccination Rate @@ -126,7 +138,7 @@ We can implement vaccine constraints by adding more model complexity. Resource limitations create an upper bound on the number of vaccines that can be administered to susceptibles per time step. There is also the constraint that we can only vaccinate, at most, the current number -of susceptibles i.e. the vaccination rate can be at most 1. These +of susceptibles i.e. the vaccination rate can be at most 1. These constraints naturally lead us to consider a variable vaccination rate $\phi(S(t))$, instead of vaccinating a fixed proportion $\phi > 0$ per time step. @@ -617,25 +629,25 @@ print(reparameterized_spec) #> --------------------- #> Default values: #> --------------------- -#> quantity value -#> a 1.684889e+04 -#> b 1.684889e+04 -#> rho 5.555556e-03 -#> beta_s 2.000000e-01 -#> beta_v 5.000000e-02 -#> alpha 3.030303e-01 -#> gamma_i 1.000000e-01 -#> gamma_h 7.000000e-02 -#> sigma 1.000000e-01 -#> N 1.480000e+08 -#> I 2.718571e+03 -#> V 1.015657e+04 -#> E 0.000000e+00 -#> H 6.300000e+01 -#> R 0.000000e+00 -#> logit_p -4.595120e+00 -#> log_beta -4.605170e+00 -#> log_E_I_ratio -4.605170e+00 +#> matrix row col value +#> a 1.684889e+04 +#> b 1.684889e+04 +#> rho 5.555556e-03 +#> beta_s 2.000000e-01 +#> beta_v 5.000000e-02 +#> alpha 3.030303e-01 +#> gamma_i 1.000000e-01 +#> gamma_h 7.000000e-02 +#> sigma 1.000000e-01 +#> N 1.480000e+08 +#> I 2.718571e+03 +#> V 1.015657e+04 +#> E 0.000000e+00 +#> H 6.300000e+01 +#> R 0.000000e+00 +#> logit_p -4.595120e+00 +#> log_beta -4.605170e+00 +#> log_E_I_ratio -4.605170e+00 #> #> --------------------- #> Before the simulation loop (t = 0): @@ -910,45 +922,45 @@ shiver_calibrator = mp_tmb_calibrator( Next we optimize, and look at our estimates. - #> mat row default estimate std.error - #> 1 time_var_rbf_beta 1 0.0000 0.2706 NaN - #> 2 time_var_rbf_beta 2 0.0000 -0.0580 0.1147 - #> 3 time_var_rbf_beta 3 0.0000 -0.0752 0.3265 - #> 4 time_var_rbf_beta 4 0.0000 0.0829 0.8638 - #> 5 prior_sd_rbf_beta 0 1.0000 0.5297 0.0177 - #> 6 distr_params_sd_H 0 1.0000 0.0732 0.0051 - #> 7 distr_params_sd_reported_incidence 0 1.0000 1.8991 0.1423 - #> 8 time_var_rbf_beta 0 0.0000 -0.4327 NaN - #> 9 beta 0 0.0100 0.8061 0.2597 - #> 10 sigma 0 0.0498 0.0004 0.0003 - #> 11 gamma_h 0 0.0498 0.0233 0.0022 - #> 12 E_I_ratio 0 0.0100 0.0839 0.1239 - #> 13 I 0 2718.5714 28127.2583 22697.4586 - #> 14 H 0 63.0000 97.0439 7.5258 - #> 15 R 0 1.0000 1.0000 54.5978 - #> 16 report_prob 0 0.5000 0.5631 0.4171 - #> 17 p 0 0.0100 0.2405 9.8432 + #> mat row default estimate std.error + #> 1 time_var_rbf_beta 1 0.0000 -0.0300 0.0487 + #> 2 time_var_rbf_beta 2 0.0000 0.0485 0.0541 + #> 3 time_var_rbf_beta 3 0.0000 -0.0695 0.0679 + #> 4 time_var_rbf_beta 4 0.0000 0.1091 0.0907 + #> 5 prior_sd_rbf_beta 0 1.0000 0.5297 0.0177 + #> 6 distr_params_sd_H 0 1.0000 0.0752 0.0157 + #> 7 distr_params_sd_reported_incidence 0 1.0000 0.2209 0.0187 + #> 8 time_var_rbf_beta 0 0.0000 -0.0270 0.0431 + #> 9 beta 0 0.0100 0.3099 0.0443 + #> 10 sigma 0 0.0498 0.0336 0.0113 + #> 11 gamma_h 0 0.0498 0.9811 0.1856 + #> 12 E_I_ratio 0 0.0100 0.0851 0.1017 + #> 13 I 0 2718.5714 2986.9423 943.6758 + #> 14 H 0 63.0000 0.1453 2.9807 + #> 15 R 0 1.0000 1.0000 54.5981 + #> 16 report_prob 0 0.5000 0.8292 0.2194 + #> 17 p 0 0.0100 0.2197 9.1710 #> conf.low conf.high - #> 1 NaN NaN - #> 2 -0.2828 1.668000e-01 - #> 3 -0.7150 5.647000e-01 - #> 4 -1.6102 1.776000e+00 + #> 1 -0.1255 6.550000e-02 + #> 2 -0.0576 1.546000e-01 + #> 3 -0.2026 6.360000e-02 + #> 4 -0.0687 2.869000e-01 #> 5 0.4951 5.643000e-01 - #> 6 0.0631 8.330000e-02 - #> 7 1.6201 2.178100e+00 - #> 8 NaN NaN - #> 9 0.4287 1.515700e+00 - #> 10 0.0001 1.600000e-03 - #> 11 0.0193 2.810000e-02 - #> 12 0.0046 1.518600e+00 - #> 13 5784.2259 1.367759e+05 - #> 14 83.3599 1.129742e+02 - #> 15 0.0000 2.978104e+46 - #> 16 0.0444 9.728000e-01 + #> 6 0.0445 1.060000e-01 + #> 7 0.1843 2.574000e-01 + #> 8 -0.1116 5.750000e-02 + #> 9 0.2342 4.102000e-01 + #> 10 0.0174 6.490000e-02 + #> 11 0.6772 1.421400e+00 + #> 12 0.0082 8.853000e-01 + #> 13 1608.0649 5.548174e+03 + #> 14 0.0000 4.193101e+16 + #> 15 0.0000 2.978526e+46 + #> 16 0.1891 9.902000e-01 #> 17 0.0000 1.000000e+00 Our prior for `sigma` is similar to the posterior, but `gamma_h` seems -to have been pushed up by the data from about `0.05` to about 0.02. We +to have been pushed up by the data from about `0.05` to about 0.98. We still do not have confidence in our estimate of `p`. We now have five other parameters controlling transmission, and so to interpret them we really need a plot of how transmission varies over time in the model. We @@ -1080,8 +1092,7 @@ for details). # References -

+