Interventions and Calibration

Once you have captured the basic dynamics of transmission using simple mathematical models, it is possible to use these models to simulate the impact of different interventions. You will study approaches for modelling treatment of infectious disease, as well as for modelling vaccination. Building on the SIR model, you will learn how to incorporate additional compartments to represent the effects of interventions (for example, the effect of vaccination in reducing susceptibility). You will learn about ‘leaky’ vaccines and how to model them, as well as different types of vaccine and treatment effects.

All models answering public health questions first need to be matched, or ‘calibrated’, against real-world data to ensure that model-simulated dynamics are consistent with what is observed. In this module, you will consider basic relationships between models and data. Using the basic SIR model that you've developed so far, you will calibrate this model to epidemic data. Through performing this calibration by hand, you'll gain an understanding of how model parameters can be adjusted so as to order to capture real-world data.

In practice model calibration for compartmental models is rarely done by hand. Rather, we construct a function that summarises the goodness-of-fit between the model and the data and then use available computer algorithms to maximise this goodness-of-fit. In these next two modules, you will learn about two simple approaches to computer-based model calibration: the least-squares approach and the maximum-likelihood approach. You will perform model calibrations under each of these approaches in R.