Second of Our UMBC Faculty DE Series
Location
Mathematics/Psychology : 401
Date & Time
November 1, 2021, 11:00 am – 12:00 pm
Description
Title: SIR model with prescribed recovery time distribution and time varying
infectivity.
infectivity.
Abstract: The traditional ODE model for the spread of an infectious disease known as the SIR (Susceptible, Infected and Recovered) model is based on certain assumptions. We describe an extension of this SIR model that takes into account the fact that an infected person has a certain probability
distribution for the recovery time. It is seen that the standard ODE model is
consistent with assuming an unrealistic exponential distribution for the
recovery time distribution. We will also expand the model by allowing
the infectivity to vary with the duration of infection in a prescribed manner.
It must be emphasized that our model is deterministic despite the
consideration of the probability distribution for recovery time.
Our modeling leads a first order PDE that is coupled with some integral
equations. The PDE can be solved explicitly using the method of
characteristics, reducing the governing equation to a single nonlinear
integral equation for the "flux of infection."
We mention how the familiar (ODE) SIR model can be recovered from this seemingly
very different model. Finally, we discuss the existence and uniqueness theory
for our generalized SIR model equation. Time permitting, we will discuss the
consistent with assuming an unrealistic exponential distribution for the
recovery time distribution. We will also expand the model by allowing
the infectivity to vary with the duration of infection in a prescribed manner.
It must be emphasized that our model is deterministic despite the
consideration of the probability distribution for recovery time.
Our modeling leads a first order PDE that is coupled with some integral
equations. The PDE can be solved explicitly using the method of
characteristics, reducing the governing equation to a single nonlinear
integral equation for the "flux of infection."
We mention how the familiar (ODE) SIR model can be recovered from this seemingly
very different model. Finally, we discuss the existence and uniqueness theory
for our generalized SIR model equation. Time permitting, we will discuss the
more realistic approach to SIR modeling via Markov processes.
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