Epidemics: a special case of an exploitative interaction.

Bubonic plague (the black death, pestilence)

Yersinia pestis

http://telemedicine.org/stamfor1.htm

Population of Europe in millions

1000 381100 481200 591300 701347 751352 501400 451430 36

http://upload.wikimedia.org/wikipedia/commons/b/b8/Black_Death.jpg

 "How many valiant men, how many fair ladies, breakfast with their kinfolk and the same night supped with their ancestors in the next world! The condition of the people was pitiable to behold. They sickened by the thousands daily, and died unattended and without help. Many died in the open street, others dying in their houses, made it known by the stench of their rotting bodies. Consecrated churchyards did not suffice for the burial of the vast multitude of bodies, which were heaped by the hundreds in vast trenches, like goods in a ships hold and covered with a little earth."

-Giovanni Boccaccio (author of The Decameron)

Dracula – the plague carrier

Ring around a rosiePocket full of posies

Ashes ashesWe all fall down

Plagues described in the old testament consistent with the black plague

First certain outbreak 430 BC in Athens estimated death toll 30% (beginning of the end of Greek Empire)

First pandemic: a series of repeated epidemics between 541 and 750 affected the Middle East to the Mediterranian (weakened the Byzantine Empire).

Second pandemic: 1346-1351. Estimated dead in China: 50%, estimated dead in Europe; 30%. Followed by cyclical outbreaks for >200 years

Third pandemic: 1855 – 1900. From China to India, Africa, Australia, Europe, Hawaii, India, Japan, the Middle East, the Philippines and North and South America

Caffa, (today’s Feodosia in the Ukraine), Genoese traders had a fortress which was besieged in 1347 by Mongol armies.

The Mongols carried the disease and catapulted dead bodies over the fortress wall.

The Genoese fled home…

After the original epidemic, it revisited Europe once in almost every generation for 600 years.

•Most cases were more localized hitting individual cities

•continuing high death toll of 30-40%

•Last outbreak of that era in Marseilles (1720), when a commercial ship

named the `Grand Saint-Antoine' arrived from Syria and Lebanon with

cases of plague aboard. This epidemic killed 50,000 people.

Questions arise from the study of European epidemics:

How do new epidemics suddenly appear?

Why do they disappear as suddenly?

Why can they come back?

Can one eradicate diseases totally?

Epidemics introduced to the Americas from Europe:

SmallpoxBubonic plagueTyphusMumpsInfluenzaYellow feverMeaslesScarlet fever

Estimated death toll uncertain. Up to 90% by some estimates.

The population biology of disease

I

S

I

infected

R

resistant

susceptible

S

dead

D

Birth rate (assumed = combined death rate) dead

D

c

bb

b

i

v

Assumption 1: total population size remains constant:

N: total population size: N = S + I + R

b: rate of mortality not due to infection

c: mortality of infecteds due to disease

a: transmission probabilityb: rate of mortality not due to infection

Susceptible loss rate = aIS + bS

Assumption 2: Susceptible-Infecteds encounter rates depend only on their respective population densities:

bSaIScIbNdt

dS

Rate of change for population of Susceptibles:

Death rate, same as birth rate

Susceptibles that become infected

Susceptibles that die of other causes

IvcbaISdt

dI)(

Rate of change for population of Infecteds:

a: transmission probabilityb: rate of mortality not due to infectionc: mortality of infecteds due to diseasev: rate of recovery

bRvIdt

dR

Rate of change for population of Recovered:

b: rate of mortality not due to infectionv: rate of recovery

The SIR model of infectious diseasewith direct transmission:

bSaIScIbNdt

dS

IvcbaISdt

dI)(

bRvIdt

dR

Two-dimensional model, because S+I+R = const.

Infectedsisocline

Susceptiblesisocline

Infe

cted

s

Susceptibles

I*

As long as I*>0, the disease stays alive.

To keep the disease alive, the equilibriumnumber of Infecteds has to be >0:

10*

vcb

aNifI

vcb

aN

is called the basic reproductive rate of the infectious disease

a

vcbN

The larger the population, the easier for the disease to survive.

To keep the disease alive, the population must exceed a minimum size.

Adding immunization:

I

S

I

infected

R

resistantS

dead

D

dead

D

immunization

The SIR model of infectious diseasewith direct transmission and immunization:

iSbSaIScIbNdt

dS

IvcbaISdt

dI)(

bRiSvIdt

dR

Infectedsisocline

Susceptibles isocline

Infe

cted

s

Susceptibles

immunizationrate

The disease dies out when I*<0. Too few Susceptibles remain to keep the disease alive.

I*

To keep the disease alive, the equilibriumnumber of Infecteds has to be >0:

1)(*)(

0*

vcbib

abNifI

vcb

vcbaNbi

)( is the critical immunization rate

that would eradicate the disease.

How do new epidemics suddenly appear?

Origins: often jump host from animal to human. Host-jumping is facilitated where people live in close quarters with livestock. Epidemics spread and evolve fast in large, concentrated population centers.

Trade, warfare, famines, which put people on the move, spread the disease away from their origin.

Disease Origin

Measles Cattle

Tuberculosis Cattle

Smallpox Cattle

Anthrax Cattle

Flu Pigs & Ducks

Whooping cough Pigs & Dogs

Malaria Chicken & Ducks

Why do they disappear as suddenly?

Why can they come back?

Can one eradicate diseases totally?

Everybody who can get infected was infected.Diseases can die out when no carrier survives.

After original infection, epidemics are prone to come every generation as Susceptibles replace Resistants in the population.

In theory, by immunization. In the US, many epidemic diseases have practically been eliminated. However, many live on in developing countries (and some in weapons laboratories).

New diseases evolve all the time.