Case Studies and Project Ideas: Yellow Fever

Yellow Fever Case Study: Philadelphia, Summer of 1793

Source

World Health Organization Website
History of 1793 outbreak

Background

Yellow fever is viral disease that has caused epidemics in Africa and the Americas. The disease is spread through a "vector", or an intermediary which transfers the disease from person to person. In the case of yellow fever, the vector is a mosquito, and the virus can be spread between people and primates. The symptoms of yellow fever vary-- upon contraction the disease incubates in the body for three to six days. Initial symptoms can include fever, muscle pain, headache, shivering, nausea, vomitting, and a slowing of the pulse. After 3 or 4 days, symptoms disappear in 85% of patients, however the other 15% enter a "toxic phase". In the toxic phase, symptoms become more severe, and can include kidney malfunction, abdominal pain, and jaundice (decreased function of the liver), which gives the virus the name "yellow." Although a vaccination has been available for 60 years, many parts of the world remain unvaccinated and epidemic outbreaks occur in tropical areas of Africa and the Americas, where the virus is endemic (always present at low levels). Yellow fever occurs in three fashions, Sylvatic (jungle) yellow fever, Intermediate yellow fever, and Urban yellow fever:

"Sylvatic (or jungle) yellow fever: In tropical rainforests, yellow fever occurs in monkeys that are infected by wild mosquitoes. The infected monkeys can then pass the virus onto other mosquitoes that feed on them. These infected wild mosquitoes bite humans entering the forest resulting in sporadic cases of yellow fever. The majority of cases are young men working in the forest (logging, etc). On occasion, the virus spreads beyond the affected individual."
"Intermediate yellow fever: In humid or semi-humid savannahs of Africa, small-scale epidemics occur. These behave differently from urban epidemics; many separate villages in an area suffer cases simultaneously, but fewer people die from infection. Semi-domestic mosquitoes infect both monkey and human hosts. This area is often called the "zone of emergence", where increased contact between man and infected mosquito leads to disease. This is the most common type of outbreak seen in recent decades in Africa. It can shift to a more severe urban-type epidemic if the infection is carried into a suitable environment (with the presence of domestic mosquitoes and unvaccinated humans)."
"Urban yellow fever: Large epidemics can occur when migrants introduce the virus into areas with high human population density. Domestic mosquitoes (of one species, Aedes aegypti) carry the virus from person to person; no monkeys are involved in transmission. These outbreaks tend to spread outwards from one source to cover a wide area."

(From World Health Organization Website)

Case Study

In August of 1793, a serious outbreak of yellow fever affected Philadelphia, which was at the time the capital of the newly formed United States of America. Yellow fever came to Philadelphia from the West Indies, ships carrying goods to Philadelphia also carried mosquitos, and because the ships were not quarantined upon entry to the port, the mosquitos were able to spread the disease quickly. Little was known about the disease and the spread of the disease was aggrevated by unsanitary conditions. The hot, dry summer conditions were ideal for mosquito proliferation, and the epidemic did not end until the fall, when cold weather killed the mosquitos off. During the epidemic over 5000 citizens were killed-- ten percent of the population at the time.

Building the Model

The yellow fever epidemic of Philadelpia models a case of Urban Yellow fever, where the populations to be considered are Human and Mosquito.

Human Model

The human part of the model is the standard SIR model, where recovery provides immunity to yellow fever. Because humans can only be infected by mosquitos and not each ofhter, the infection rate is affected by the number of infected mosquitos, the number of susceptible humans, and the rate of infection. Once infected, they can either die of yellow fever, of other causes, or recover and be immune. Once immune, they can die of other causes, but will not return to susceptibility.

Mosquito Model

In the mosquito part of the model, the mosquitos can either be healthy or infected with the yellow fever virus. The infection of mosquitos is based on the number of infected humans and the rate of infection from humans to mosquitos. The death rate is the same for infected and for healthy mosquitos as they are not affected by the yellow fever virus.

Equations and Constants

dS/dt = b*t - [i*(Y/M)*(S/T)] - S*d

dI/d = [i*(Y/M)*(S/T)] - r*I - d*I - f*I

dIM/dt = r*I - IM*d

dH/dt = (c*M) - [g*H*(I/T)] - H*j

dY/dt = [g*H*(I/T)] - H*j

b = human birth rate

i = human infection constant

T = total human population

M = total mosquito population

d = natural human death rate

r = recovery rate

f = yellow fever death rate

c = mosquito birth rate

g = mosquito infection constant

j = mosquito death rate

Initial Values

b = .05

i = 16000

d = .05

r = .05

f = .1

c = .2

g = .2

j = .2

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