Epidemiological model provided by the package

The basic epidemiological model in the package is a SEEIIR model, which is a version of the SEIR model, but with both the Exposed and Infected split into two different groups. This results in a more realistic gamma distributed waiting time both between the exposed and infected state and the infected and recovered states.

We also need to keep track of who is vaccinated or not. When a Susceptible is vaccinated there is a certain probability that the person becomes recovered (and vaccinated), or stays susceptible (but vaccinated). This is dependent on the efficacy of the vaccine that season. Once one is in any of the other states, we assume that the vaccine does not influence the progress of the infection. As a result an infected who is vaccinated, will stay infected, but is now also tracked as being vaccinated.

Finally we divide the population into different age groups and risk groups. Different age groups and risk groups will be vaccinated at different rates. Infections between age groups happens according to the a contact matrix. The contact matrix governs the number of contacts between and within people of different age groups.

The main function implementing the epidemiological model is the infectionODEs function. This function requires a number of parameters and we will explain all these parameters below.

infectionODEs(population, initial_infected, vaccine_calendar, contact_matrix,
  susceptibility, transmissibility, infection_delays, interval)

library(fluEvidenceSynthesis)
data(demography) # Population divided by age (0 years old, 1 years old, etc.)

# Separate into non elderly (<65) and elderly population
ag <- stratify_by_age(demography, limits=c(65)) # c( 43670500, 8262600 )

# Separate in risk groups. In this case we assume one additional (high) risk groups and that respectively 
# 1 percent of non elderly and 40% of elderly are in this risk group. It is possible to
# define an additional risk group (e.g. pregnant women) if desired
population <- stratify_by_risk(ag, matrix(c(0.01,0.4),nrow=1), 
                                labels = c("LowRisk", "HighRisk")) # c( 43233795, 4957560, 436705, 3305040 )

library(fluEvidenceSynthesis)
ag <- c(1000,1000)
initial.infected <- stratify_by_risk( ag, matrix(c(0.01,0.4),nrow=1)) # c(990, 600, 10, 400)

vaccine_calendar <- as_vaccination_calendar(
  efficacy = c(0.7,0.3),
  coverage = as.data.frame(matrix(c(0,0,0,0,0,0.861,0.123,0.861), nrow = 2, byrow = T)),
  dates = c(as.Date("2010-10-01"), as.Date("2011-02-01")), # begin and end date
  no_age_groups = 2,
  no_risk_groups = 2
)

library(fluEvidenceSynthesis)
data(polymod_uk)
data(demography)

# Polymod data is subdivided in seven age groups
poly <- polymod_uk[,c(1,2,3,9)]
poly[,3] <- rowSums(polymod_uk[,3:8])

contacts <- contact_matrix(as.matrix(poly), demography, c(65))
pander(contacts)

susceptibility <- c( 0.7, 0.3 ) # Different for different ages
transmissibility <- 0.17 # Same for all ages
infection_delays <- c( 0.8, 1.8 ) # 0.8 and 1.8 day.

Run the model

odes <- infectionODEs( population, initial.infected, vaccine_calendar, contacts, 
               susceptibility, transmissibility, infection_delays, 7 )
pander(head(odes))

Time	LowRisk [0,65)	LowRisk [65,+)	HighRisk [0,65)	HighRisk [65,+)
2010-09-06	5820	721.5	58.79	481
2010-09-13	8888	169.7	89.78	113.1
2010-09-20	13996	266.9	141.4	177.9
2010-09-27	22011	419.8	222.3	279.9
2010-10-04	34551	658.7	348.9	439.1
2010-10-11	54060	1019	543.7	679.3

fraction.infected <- odes %>%
  gather(Group, Incidence, -Time) %>%
  mutate(fraction = Incidence/population[Group])

ggplot( data=fraction.infected ) + geom_line( aes(x=Time, y=fraction, colour = Group) ) + 
  ylab( "Fraction infected" )

Fraction infected for each group. Note that the results for both risk groups for ages 65+ are the same and therefore cover each other

Further reading

You can look up how to adapt the underlying transmission model to your own needs in the adapting-the-transmission-model vignette or learn how to use your model for parameter inference, which is explained in more detail in the inference vignette.