SIR modeling

infectious disease

illness due to specific infectious agent or its toxic products that arises through transmission of that agent or its products from an infected person, animal, or resrvoir to a susceptible host, either directly or indirectly through an intermediate plant or animal host, vector, or the environment

exposed

an individual who has met with an infectious agent in a way that we know from experience may cause disease.

classification of periods during an infection based on clinical signs

incubation, subclinical, or clinical infection

classification of periods during an infection based on contagiousness

non infectious (including the latent period) and infectious

mutually exclusive groups

SI model

susceptible to infectious

SIS

susceptible will be infectious then susceptible

no immunity and will go back to susceptibility

SIR

susceptible will be infectious and then will recover

recovery period

will not be available to be infected again

SIRS

susceptible will be infectious and then recovered and then will be susceptible again

Have immunity to recover

SEIR

susceptible to infected to infectious to recovered

SEIRS

susceptible to infected to infectious to recovered to susceptible

infected period relates to the

latent period

what models dont have a latent period

SI

SIS
SIR

SIRS

R0

basic reproduction number that is the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population

what does R0 describe

the propensity for a contagious disease to spread from individual to individual in a population

what does R0 depend on

c and p

what does R0 say about the infection spread

some infections have faster speed than others so will only be considered when talking about two different infections

Re

effective reproduction number that we use during an outbreak

Re=

R0x where x us the fraction of the host population that is susceptible

Re

During an outbreak, once the infection takes its course in a population the number of susceptibles declines and so does the “speed” of infection spread. By definition, the measure of R0 could no longer be used and we use a related measure:

H=

1 - 1/R0

H

herd immunity threshold

higher the R0, the

more effort needed for vaccination

you dont need to vaccinate the

whole population, but most

how can you make models better

add more factors (SIRS, environment factors, etc) to make it more realistic and useful