Relative susceptible by interaction (#148)

* Bugfix - remove occupation network from params object once set up

If model is created multiple times from the same params object then we
get different answers. Problem with the Simulation Python interface, but
not the Model Python interface (so was missed in tests).

* Make releative_susceptibility_xxxx per interaction not per day

Remove the normalisation to the based on the mean number of interactions
to the adjusted susceptibility

* Update baseline parameters for asypmtomatic, mild and hospitalised

* Change equation to normalise by mean interactions

Not mean interactions by age

* Update doc with hew def of relative susceptibility

* Update realtive severity infectiousness data with Sun data

* Update the header of set_up_infectious_curves

Remove the text saying we adjust by mean interactions for the age group

* Update with calibrated infectious parameter and lockdown rate

* Increase number of cases in test_disease_transition_times

Test failing with a very small number of cases leading to inaccuracy

* Decrease the infectious rate to reduce saturation effect

test_relative_transmission_update is running in to saturation effect
with the updated params

Author: roberthinch

documentation/covid19.md

@@ -126,7 +126,7 @@ Combining all effects, we model the rate at which the virus is transmitted in a
 
 <p><img src="eqn_transmission_rate.png" height="80"></p>
 
-where *t* is the time since infection; *s<sub>i</sub>* indicates the infector's symptom status (asymtomatic, mild, moderate/severe); *a<sub>s</sub>* is the age of the susceptible; *n* is the type of network where the interaction occurred; *I<sub>a<sub>s</sub></sub>* is the mean number of daily interactions for somebody of the age of the susceptible; *f<sub>&#915;</sub>(u; &#956;,&#963;<sup>2</sup>)* is the probability density function of a gamma distribution; *&#956;<sub>i</sub>* and *&#963;<sub>i</sub>* are the mean and width of the infectiousness curve; *R* scales the overall infection rate (under some simplifying assumptions it is mean number of people infected by each moderately/severely symptomatic individual); *S<sub>a<sub>s</sub></sub>* is the scale-factor for the age of the susceptible; *A<sub>s<sub>i</sub></sub>* is the scale-factor for the infector being asymptomatic; *B<sub>n</sub>* is the scale-factor for the network on which the interaction occurred.
+where *t* is the time since infection; *s<sub>i</sub>* indicates the infector's symptom status (asymtomatic, mild, moderate/severe); *a<sub>s</sub>* is the age of the susceptible; *n* is the type of network where the interaction occurred; *I* is the mean number of daily interactions; *f<sub>&#915;</sub>(u; &#956;,&#963;<sup>2</sup>)* is the probability density function of a gamma distribution; *&#956;<sub>i</sub>* and *&#963;<sub>i</sub>* are the mean and width of the infectiousness curve; *R* scales the overall infection rate (under some simplifying assumptions it is mean number of people infected by each moderately/severely symptomatic individual); *S<sub>a<sub>s</sub></sub>* is the scale-factor for the age of the susceptible; *A<sub>s<sub>i</sub></sub>* is the scale-factor for the infector being asymptomatic; *B<sub>n</sub>* is the scale-factor for the network on which the interaction occurred.
 Table [Infection parameters](./parameters/infection_parameters.md) contains the values of the parameters used in simulations.
 The rate of virus transmission is converted to a probability of transmission
 

documentation/eqn_transmission_rate.png

@@ -10,35 +10,35 @@
 | `sd_time_to_recover` | 5 | &#963;<sub>rec</sub> | Standard deviation of time to recovery if hospitalisaion is not required (days) | Yang et al 2020 |
 | `mean_time_to_death` | 11.74 | &#956;<sub>death</sub> | Mean time to death after acquiring critical care (days) | Personal communication with SPI-M; data soon to be published |
 | `sd_time_to_death` | 8.79 | &#963;<sub>death</sub> | Standard deviation of time to death after acquiring critical care (days) | Personal communication with SPI-M; data soon to be published |
-| `fraction_asymptomatic_0_9` | 0.605 | &#966;<sub>asym</sub>(0-9) | Fraction of infected individuals who are asymptomatic, aged 0-9 | - |
-| `fraction_asymptomatic_10_19` | 0.546 | &#966;<sub>asym</sub>(10-19) | Fraction of infected individuals who are asymptomatic, aged 10-19 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `fraction_asymptomatic_20_29` | 0.483 | &#966;<sub>asym</sub>(20-29) | Fraction of infected individuals who are asymptomatic, aged 20-29 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `fraction_asymptomatic_30_39` | 0.418 | &#966;<sub>asym</sub>(30-39) | Fraction of infected individuals who are asymptomatic, aged 30-39 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `fraction_asymptomatic_40_49` | 0.354 | &#966;<sub>asym</sub>(40-49) | Fraction of infected individuals who are asymptomatic, aged 40-49 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `fraction_asymptomatic_50_59` | 0.294 | &#966;<sub>asym</sub>(50-59) | Fraction of infected individuals who are asymptomatic, aged 50-59 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `fraction_asymptomatic_60_69` | 0.242 | &#966;<sub>asym</sub>(60-69) | Fraction of infected individuals who are asymptomatic, aged 60-69 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `fraction_asymptomatic_70_79` | 0.199 | &#966;<sub>asym</sub>(70-79) | Fraction of infected individuals who are asymptomatic, aged 70-79 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `fraction_asymptomatic_80` | 0.163 | &#966;<sub>asym</sub>(80) | Fraction of infected individuals who are asymptomatic, aged 80+ | - |
-| `mild_fraction_0_9` | 0.387 | &#966;<sub>mild</sub>(0-9) | Fraction of infected individuals with mild symptoms, aged 0-9 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_10_19` | 0.435 | &#966;<sub>mild</sub>(10-19) | Fraction of infected individuals with mild symptoms, aged 10-19 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_20_29` | 0.478 | &#966;<sub>mild</sub>(20-29) | Fraction of infected individuals with mild symptoms, aged 20-29 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_30_39` | 0.512 | &#966;<sub>mild</sub>(30-39) | Fraction of infected individuals with mild symptoms, aged 30-39 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_40_49` | 0.532 | &#966;<sub>mild</sub>(40-49) | Fraction of infected individuals with mild symptoms, aged 40-49 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_50_59` | 0.541 | &#966;<sub>mild</sub>(50-59) | Fraction of infected individuals with mild symptoms, aged 50-59 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_60_69` | 0.543 | &#966;<sub>mild</sub>(60-69) | Fraction of infected individuals with mild symptoms, aged 60-69 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_70_79` | 0.541 | &#966;<sub>mild</sub>(70-79) | Fraction of infected individuals with mild symptoms, aged 70-79 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
-| `mild_fraction_80` | 0.534 | &#966;<sub>mild</sub>(80) | Fraction of infected individuals with mild symptoms, aged 80+ | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_0_9` | 0.456 | &#966;<sub>asym</sub>(0-9) | Fraction of infected individuals who are asymptomatic, aged 0-9 | - |
+| `fraction_asymptomatic_10_19` | 0.412 | &#966;<sub>asym</sub>(10-19) | Fraction of infected individuals who are asymptomatic, aged 10-19 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_20_29` | 0.370 | &#966;<sub>asym</sub>(20-29) | Fraction of infected individuals who are asymptomatic, aged 20-29 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_30_39` | 0.332 | &#966;<sub>asym</sub>(30-39) | Fraction of infected individuals who are asymptomatic, aged 30-39 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_40_49` | 0.296 | &#966;<sub>asym</sub>(40-49) | Fraction of infected individuals who are asymptomatic, aged 40-49 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_50_59` | 0.265 | &#966;<sub>asym</sub>(50-59) | Fraction of infected individuals who are asymptomatic, aged 50-59 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_60_69` | 0.238 | &#966;<sub>asym</sub>(60-69) | Fraction of infected individuals who are asymptomatic, aged 60-69 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_70_79` | 0.214 | &#966;<sub>asym</sub>(70-79) | Fraction of infected individuals who are asymptomatic, aged 70-79 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `fraction_asymptomatic_80` | 0.192 | &#966;<sub>asym</sub>(80) | Fraction of infected individuals who are asymptomatic, aged 80+ | - |
+| `mild_fraction_0_9` | 0.533 | &#966;<sub>mild</sub>(0-9) | Fraction of infected individuals with mild symptoms, aged 0-9 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_10_19` | 0.569 | &#966;<sub>mild</sub>(10-19) | Fraction of infected individuals with mild symptoms, aged 10-19 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_20_29` | 0.597 | &#966;<sub>mild</sub>(20-29) | Fraction of infected individuals with mild symptoms, aged 20-29 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_30_39` | 0.614 | &#966;<sub>mild</sub>(30-39) | Fraction of infected individuals with mild symptoms, aged 30-39 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_40_49` | 0.616 | &#966;<sub>mild</sub>(40-49) | Fraction of infected individuals with mild symptoms, aged 40-49 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_50_59` | 0.602 | &#966;<sub>mild</sub>(50-59) | Fraction of infected individuals with mild symptoms, aged 50-59 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_60_69` | 0.571 | &#966;<sub>mild</sub>(60-69) | Fraction of infected individuals with mild symptoms, aged 60-69 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_70_79` | 0.523 | &#966;<sub>mild</sub>(70-79) | Fraction of infected individuals with mild symptoms, aged 70-79 | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
+| `mild_fraction_80` | 0.461 | &#966;<sub>mild</sub>(80) | Fraction of infected individuals with mild symptoms, aged 80+ | Calibration of Riccardo et al. 2020 & Spanish Serology Survey |
 | `mean_asymptomatic_to_recovery` | 15 | &#956;<sub>a,rec</sub> | Mean time from infection to recovery (and no longer infectious) for an asymptomatic individual (days) | Yang et al 2020 |
 | `sd_asymptomatic_to_recovery` | 5 | &#963;<sub>a,rec</sub> | Standard deviation from infection to recovery for an asymptomatic individual (days) | Yang et al 2020 |
-| `hospitalised_fraction_0_9` | 0.002 | &#966;<sub>hosp</sub>(0-9) | Fraction of infected individuals with severe symptoms aged 0-9 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_10_19` | 0.009 | &#966;<sub>hosp</sub>(10-19) | Fraction of infected individuals with severe symptoms aged 10-19 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_20_29` | 0.017 | &#966;<sub>hosp</sub>(20-29) | Fraction of infected individuals with severe symptoms aged 20-29 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_30_39` | 0.065 | &#966;<sub>hosp</sub>(30-39) | Fraction of infected individuals with severe symptoms aged 30-39 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_40_49` | 0.186 | &#966;<sub>hosp</sub>(40-49) | Fraction of infected individuals with severe symptoms aged 40-49 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_50_59` | 0.231 | &#966;<sub>hosp</sub>(50-59) | Fraction of infected individuals with severe symptoms aged 50-59 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_60_69` | 0.324 | &#966;<sub>hosp</sub>(60-69) | Fraction of infected individuals with severe symptoms aged 60-69 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_70_79` | 0.387 | &#966;<sub>hosp</sub>(70-79) | Fraction of infected individuals with severe symptoms aged 70-79 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
-| `hospitalised_fraction_80` | 0.439 | &#966;<sub>hosp</sub>(80) | Fraction of infected individuals with severe symptoms aged 80+ who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_0_9` | 0.001 | &#966;<sub>hosp</sub>(0-9) | Fraction of infected individuals with severe symptoms aged 0-9 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_10_19` | 0.006 | &#966;<sub>hosp</sub>(10-19) | Fraction of infected individuals with severe symptoms aged 10-19 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_20_29` | 0.015 | &#966;<sub>hosp</sub>(20-29) | Fraction of infected individuals with severe symptoms aged 20-29 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_30_39` | 0.069 | &#966;<sub>hosp</sub>(30-39) | Fraction of infected individuals with severe symptoms aged 30-39 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_40_49` | 0.219 | &#966;<sub>hosp</sub>(40-49) | Fraction of infected individuals with severe symptoms aged 40-49 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_50_59` | 0.279 | &#966;<sub>hosp</sub>(50-59) | Fraction of infected individuals with severe symptoms aged 50-59 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_60_69` | 0.370 | &#966;<sub>hosp</sub>(60-69) | Fraction of infected individuals with severe symptoms aged 60-69 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_70_79` | 0.391 | &#966;<sub>hosp</sub>(70-79) | Fraction of infected individuals with severe symptoms aged 70-79 who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
+| `hospitalised_fraction_80` | 0.379 | &#966;<sub>hosp</sub>(80) | Fraction of infected individuals with severe symptoms aged 80+ who are hospitalised | Calibration of Riccardo et al. 2020 & Spanish Serology Survey & Ferguson et al. 2020 |
 | `critical_fraction_0_9` | 0.05 | &#966;<sub>crit</sub>(0-9) | Fraction of hospitalised individuals aged 0-9 who need critical care | Ferguson et al, 2020 |
 | `critical_fraction_10_19` | 0.05 | &#966;<sub>crit</sub>(10-19) | Fraction of hospiatlised individuals aged 10-19 who need critical care | Ferguson et al, 2020 |
 | `critical_fraction_20_29` | 0.05 | &#966;<sub>crit</sub>(20-29) | Fraction of hospitalised individuals aged 20-29 who need critical care | Ferguson et al, 2020 |

documentation/parameters/disease_dynamics_parameters.md

@@ -4,9 +4,9 @@
 | `n_seed_infection` | 5 | - | Number of infections seeded at simulation start | - |
 | `mean_infectious_period` | 5.5 | μ | Mean of the generation time distribution (days) | Ferretti et al in prep 2020; Ferretti & Wymant et al 2020; Xia et al 2020; He et al 2020; Cheng et al 2020 |
 | `sd_infectious_period` | 2.14 | σ | Standard deviation (days) of infectious period | Ferretti et al in prep 2020; Ferretti & Wymant et al 2020; Xia et al 2020; He et al 2020; Cheng et al 2020 |
-| `infectious_rate` | 5.64 | *R* | Mean number of individuals infected by each infectious individual with moderate to severe symptoms | Derived from calibration |
-| `asymptomatic_infectious_factor` | 0.29 | *A<sub>asym</sub>* | Infectious rate of asymptomatic individuals relative to symptomatic individuals | Luo et al 2020 |
-| `mild_infectious_factor` | 0.48 | *A<sub>mild</sub>* | Infectious rate of mildly symptomatic individuals relative to symptomatic individuals | Luo et al 2020 |
+| `infectious_rate` | 5.18 | *R* | Mean number of individuals infected by each infectious individual with moderate to severe symptoms | Derived from calibration |
+| `asymptomatic_infectious_factor` | 0.33 | *A<sub>asym</sub>* | Infectious rate of asymptomatic individuals relative to symptomatic individuals | Personal communication, Sun |
+| `mild_infectious_factor` | 0.72 | *A<sub>mild</sub>* | Infectious rate of mildly symptomatic individuals relative to symptomatic individuals | Personal communction, Sun |
 | `relative_susceptibility_0_9` | 0.35 | *S<sub>0-9</sub>* | Relative susceptibility to infection, aged 0-9 | Zhang et al. 2020 |
 | `relative_susceptibility_10_19` | 0.69 | *S<sub>10-19</sub>* | Relative susceptibility to infection, aged 10-19 | Zhang et al. 2020 |
 | `relative_susceptibility_20_29` | 1.03 | *S<sub>20-29</sub>* | Relative susceptibility to infection, aged 20-29 | Zhang et al. 2020 |