# DE Seminar: Prof. Muruhan Rathinam (UMBC)

### 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.

**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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