By now we know how to code a compartmental model. We also know what an SIR model is and what are its main building blocks. In this exercise we will build on our previous code to construct a fully dynamic SIR model.
1. Building an SIR model
Case study: a new virus X2021 has been identified in your town and is currently causing an outbreak. You have been commissioned by WHO to provide modelling projections to have a broad idea of the potential size of this outbreak. The ongoing epidemiological investigation have identified the following facts that might guide you in your model development:
1) The virus transmits from human to human via micro droplets from the respiratory tract.
2) Once infection is established infected individuals remain infectious for an average period of 6 days
3) From a previous outbreak of X2021 in a neighboring town we know that the CFR is ~15%
4) No known factors have been identified for increased susceptibility in any particular population group
5) From the same previous outbreak, an infection rate of 0.5 per day (CI95% 0.3 to 0.6) has been estimated
Task: Using the code below (from our previous session) build an SIR model that reflects the case above and try to answer the following questions, providing a :
1) When do we expect the X2021 outbreak to peak (in days) ?
2) How many people do we expect to get infected at the end of the outbreak?
3) Can you provide a range for the final size of the epidemic (number infected) and the expected peak (in days) based in the uncertainty around the infection rate?
Note: Copy the code below into your R Studio session. Try to fill the gaps marked with ??
Analysis of SIR assumptions
Think about the main assumptions and concepts reviewed in our lesson and try to answer:
1) Why is the homogeneous assumption of risk of infection a simplification and what factors can affect this? What are potential sources of heterogeneity?
2) What factors might affect our assumption of a homogeneous p across the population?