PyRoss: Infectious disease models in Python
PyRoss is a numerical library for mathematical modelling of infectious disease in Python. Currently the library supports structured compartment models formulated as systems of differential equations.
The library was developed to model the outbreak of the novel coronavirus COVID-19 and to assess the age-structured impact of social distancing measures in India.
The library is named after Sir Ronald Ross, doctor, mathematician and poet. In 1898 he made "the great discovery" in his laboratory in Calcutta "that malaria is conveyed by the bite of a mosquito". He won the Nobel Prize in 1902 and laid the foundations of the mathematical modelling of infectious diseases.
- Age-structured impact of social distancing on the COVID-19 epidemic in India, Rajesh Singh and R. Adhikari, arXiv:2003.12055.
Our latest forecast using case data until 25-03-2020:
Clone (or download) the repository and use a terminal to install using
>> git clone https://github.com/rajeshrinet/pyross.git >> cd pyross >> python setup.py install
PyRoss requires the following software
The age and social contact data that is needed to construct structured compartment models can be found at the following sources:
Age structure: Population Pyramid website.
Contact structure: Projecting social contact matrices in 152 countries using contact surveys and demographic data, Kiesha Prem, Alex R. Cook, Mark Jit, PLOS Computational Biology, (2017) DOI, Supporting Information Text and Supporting Information Data.
The list of COVID-19 cases is obtained from the Worldometer website.
#Ex1: M=1 import numpy as np import pyross M = 1 # the SIR model has no age structure Ni = 1000*np.ones(M) # so there is only one age group N = np.sum(Ni) # and the total population is the size of this age group beta = 0.2 # infection rate gamma = 0.1 # recovery rate alpha = 0 # fraction of asymptomatic infectives fsa = 1 # the self-isolation parameter Ia0 = np.array() # the SIR model has only one kind of infective Is0 = np.array() # we take these to be symptomatic R0 = np.array() # and assume there are no recovered individuals initially S0 = N-(Ia0+Is0+R0) # so that the initial susceptibles are obtained from S + Ia + Is + R = N # there is no contact structure def contactMatrix(t): return np.identity(M) # duration of simulation and data file Tf = 160; Nt=160; filename = 'this.mat' # instantiate model model = pyross.models.SIR(alpha, beta, gamma, fsa, M, Ni) # simulate model model.simulate(S0, Ia0, Is0, contactMatrix, Tf, Nt, filename)
See the examples folder for a list of worked out examples.