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Infectious Disease Epidemiology and Transmission Dynamics: COVID 19

HOW TO LEARN ->

Coronavirus disease 2019 (COVID-19) is an infectious

disease caused by SARS-CoV-2,a virus closely related to the SARS

virus.The disease is the cause of the 2019–20 coronavirus outbreak. It

is primarily spread between people by small droplets from infected

individuals when they breathe or cough. Time from exposure to onset

of symptoms is generally between 2 and 14 days.Spread can belimited by handwashing and other hygiene measures.

SARS = Severe acute respiratory syndrome

Population dynamics of infectious diseases

Terminology

•Endemic - habitual presence of a disease within a given area•Epidemic - occurrence of a disease in a region in excess of normal•Pandemic - worldwide epidemic

Causes of diseases• Bacteria - single-celled, no nucleus

• Virus - sub-microscopic infectious agent that can’t survive outside a host cell

• Environmental - non-biological agent such as a toxic substance

• Genetic - hereditary disease from genetic defects

• Prion - Abnormal proteins

• Protist - diverse group of eukaryotic microorganisms

• Fungi and more

Modes of Transmission

• Direct - person to person• Airborne transmission• Droplet transmission• Fecal-oral transmission• Sexually transmission• Blood-borne transmission

Population dynamics of infectious diseases

SIR Models

Population consists of:

Susceptible Infectious Recovered

individuals

Spread of SARS Disease• The first case of SARS (several acute respiratory syndrome) occurred in

November, 2002 in southern China. SARS is spread by close personal contact and perhaps by airborne transmission. It was contained by July, 2003, but resulted in 812 deaths.

• Many models of the spread of disease (including SARS model) are extensions of SIR Model (three populations are considered: Susceptible, Infected, Recovered).

• In SIR Model, assume the rate of change of the number of recovered is proportional to the number of infected.

Key time periods for an infectious disease

Giesecke, J. Modern Infectious Disease Epidemiology. 2002.

Mathematical Model of Transmission Dynamics: Susceptible-Infectious-Recovered (SIR) model

• Assumptions• Population is fixed (no entries/births or departures/deaths)• Latent period is zero • Infectious period = disease duration• After recovery, individuals are immune

• People can be in one of three states• Susceptible to the infection (S)• Infected and infectious (I)• Recovered/immune (R*)

Giesecke J. Modern Infectious Disease Epidemiology. 2002. pp. 126-130

* Not to be confused with R denoting reproductive number… unfortunate nomenclature!

Susceptible

(S)

Infected

(I)

Recovered

(R)

1

2

Rate of change Proportion in state at time t

dS/dt = - βcSI

1 OUT

dI/dt = + βcSI – I/D

1 IN 2 OUT

dR/dt = + I/D

2 IN

St = St-1 - βcSt-1It-1

It = It-1 + βcSt-1It-1 – It-1/D

Rt = Rt-1 + It-1/D

Determinants of R0

For a pathogen with direct person-to-person transmission

R0 = βcD

where β is the probability of transmission per contact between infected and susceptible persons

c is the contact rate

D is the duration of infectivity

Anderson RM. Transmission dynamics of sexually transmitted infections. In: Sexually Transmitted Diseases. Holmes KK et al., eds. 1999. pp. 25-37

β

Example SIR Model

• Consider the following values• N = 1000 people• Transmission probability, β = 0.15• Contact rate, c = 12 contacts per week• Infection duration, D = 1 week

• Basic reproductive rate: R0 = 0.15 * 12 * 1 = 1.8

• Effective reproductive rate at time t: Rt = St * R0

Spread of Disease

The basic reproductive ratioR๐

Defined as

“the average number of

secondary infections caused by a single infectious individual during

their entire infectious lifetime.”

“One of the foremost and most valuable

ideas that mathematical thinking has

brought to epidemic theory”

(Heesterbeek & Dietz, 1996).

A threshold criterion

End of Lecture