SIR Epidemiology model¶
-
class
pints.toy.
SIRModel
(y0=None)[source]¶ The SIR model of infectious disease models the number of susceptible (S), infected (I), and recovered (R) people in a population [1], [2].
The particular model given here is analysed in [3],_ and is described by the following three-state ODE:
\[ \begin{align}\begin{aligned}\dot{S} = -\gamma S I\\\dot{I} = \gamma S I - v I\\\dot{R} = v I\end{aligned}\end{align} \]Where the parameters are
gamma
(infection rate), andv
, recovery rate. In addition, we assume the initial value of S,S0
, is unknwon, leading to a three parameter model(gamma, v, S0)
.The number of infected people and recovered people are observable, making this a 2-output system. S can be thought of as an unknown number of susceptible people within a larger population.
The model does not account for births and deaths, which are assumed to happen much slower than the spread of the (non-lethal) disease.
Real data is included via
suggested_values()
, which was taken from [3], [4], [5].Extends
pints.ForwardModel
, pints.toy.ToyModel.Parameters: y0 – The system’s initial state, must have 3 entries all >=0. References
[1] A Contribution to the Mathematical Theory of Epidemics. Kermack, McKendrick (1927) Proceedings of the Royal Society A. https://doi.org/10.1098/rspa.1927.0118 [2] https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology [3] (1, 2) Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. Toni, Welch, Strelkowa, Ipsen, Stumpf (2009) J. R. Soc. Interface. https://doi.org/10.1098/rsif.2008.0172 [4] (1, 2) A mathematical model of common-cold epidemics on Tristan da Cunha. Hammond, Tyrrell (1971) Epidemiology & Infection. https://doi.org/10.1017/S0022172400021677 [5] (1, 2) Common colds on Tristan da Cunha. Shybli, Gooch, Lewis, Tyrell (1971) Epidemiology & Infection. https://doi.org/10.1017/S0022172400021483