Abstract
The aim of this paper is to present a review on the stochastic version of the deterministic SIR (Susceptible – Infectious - Recovery) epidemiological compartment model through the branching process approximation. The stochastic process (branching process) approximation was developed using the Continuous Time Markov Chains where the time variable is continuous and the state variable is discrete. The state random variables are the compartments: S(t), I(t) and R(t). In this review two ways of estimating the state transition probability has been provided and some stochastic thresholds of the branching process (basic reproduction number, Malthusian parameter and the average number of infections produced by an infectious individual in a single generation) have also been deduced. Finally, the probability of major and minor outbreak of the branching process (epidemic process) has been presented. The theoretical methods have also been validated with some examples of numerical simulations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Communications in Mathematical Biology and Neuroscience
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.