This app links the reproductive number and ID control. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab. Before going through this app, you should go through the ‘Reproductive Number’ apps first.
For this app, we’ll use the same basic compartmental SIR model as for the ‘Reproductive Number 2’ app. We allow for 3 different stages/compartments:
In addition to specifying the compartments of a model, we need to specify the dynamics determining the changes for each compartment. Broadly speaking, some processes increase the number of individuals in a given compartment/stage and other processes that lead to a reduction. Those processes are sometimes called inflows and outflows.
For our system, we specify the following processes/flows:
The flow diagram and the set of equations which are used to implement this model are as follows:
Flow diagram for this model.
\[\dot S =m - b SI - nS + wR\] \[\dot I = b S I - g I - nI\] \[\dot R = g I - nR - wR\] \[S_{v} = (1-ef)S(0)\] \[R(0) = efS_{v}\]
Here, S(0) is the initial population of susceptibles, and Sv is the susceptible population left after vaccinating a fraction f. Vaccinated individuals are moved to the R compartment before the start of the outbreak, R(0). Note the unfortunate fact that the recovered compartment uses the same letter as the reproductive number, and the starting value for the R compartment, R(0) looks similar to the basic reproductive number. This is common notation and I therefore use it here too. Just be careful to make sure you know which quantity is discussed.
The tasks below are described in a way that assumes everything is in units of MONTHS (rate parameters, therefore, have units of inverse months). If any quantity is not given in those units, you need to convert it first (e.g. if it says a year, you need to convert it to 12 months).
Note that in this model, we can’t distinguish between interventions that target susceptibles or infected, both could reduce the transmission rate. Targeting susceptibles before they become infected is of course preferable, but there are usually many more of those, so targeting infected is often easier. Interventions that reduce contact and transmission/infection risk for both groups is of course best.
simulate_reproductivenumber_ode
. You can call them directly, without going through the shiny app. Use the help()
command for more information on how to use the functions directly. If you go that route, you need to use the results returned from this function and produce useful output (such as a plot) yourself.vignette('DSAIDE')
into the R console.Fine, Paul, Ken Eames, and David L Heymann. 2011. “"Herd Immunity": A Rough Guide.” Clinical Infectious Diseases : An Official Publication of the Infectious Diseases Society of America 52 (7): 911–16. https://doi.org/10.1093/cid/cir007.
Heffernan, J M, R J Smith, and L M Wahl. 2005. “Perspectives on the Basic Reproductive Ratio.” Journal of the Royal Society, Interface 2 (4): 281–93. https://doi.org/10.1098/rsif.2005.0042.
Keeling, Matt J, and Pejman Rohani. 2008. Modeling Infectious Diseases in Humans and Animals. Princeton University Press.
Roberts, M G. 2007. “The Pluses and Minuses of R0.” Journal of the Royal Society, Interface 4 (16): 949–61. https://doi.org/10.1098/rsif.2007.1031.
Vynnycky, Emilia, and Richard White. 2010. An Introduction to Infectious Disease Modelling. Oxford University Press.
Wallinga, J., and M. Lipsitch. 2007. “How generation intervals shape the relationship between growth rates and reproductive numbers.” Proceedings of the Royal Society B 274 (1609): 599–604.