Ecology of infectious diseases I Flashcards
Infectious disease is
the product of an interaction between two species; the pathogen and the host
The host is a
resource for the pathogen
y
proportion of the population that are infectious
Give the equation for the tate of change of proportion of the population that are infectious
dy/dt = lambda(1-y) - mu x y
OR
dy/dt = By(1-y) - mu x y
lambda
force of infection
force
per capita risk
B in equation
y / lambda
B in words
a combination of parameters relating risk of infection to prevalence of infection
Give the equation for B in directly transmitted pathogens
B = beta x N
N
population size
Beta
probability of transmission
For directly transmitted pathogens, lambda =
beta x Ny
Give the equation for lambda for sexually transmitted infections
lambda = c x beta x y
where y = the probability a partner is infected
and beta is the per partnership probability of infection
c
average no. of partners
Give the equation for lambda for vector-borne pathogens
lambda = ma^2bcHy
m =
number of vectors per host
a =
biting rate
b =
proportion of infectious bites leading to infection
c =
proportion of bites on infectious hosts leading to infection
H =
average lifespan of vector
Give the equation for B for vector-borne pathogens
B = ma2bcH
mu =
death rate of host
What is the equation for the plateau in a graph that measures proportion infected against time in arbitrary units
1 - (mu/B)
Or
1 - (1/R0)
Describe the pathogenesis of Herpes Simples Virus
- subvirus enters peripheral sensory nerves
- migrates along axons to sensory nerve ganglia in the CNS
- allows virus to escape immune response, and become latent
What happens post-latency
reactivation and spread to the surface for viral shedding
Describe the VZV, EBV, CMV, HHV6 and HHV7 Herpesviruses
Primary infection generally occurs in a subclinical fashion in early childhood, with subsequent lifelong persistence of infection.
Chickenpox
Varicella zoster virus
A pathogen cannot invade a population unless
- dy/dt > 0 when y = 0 (OR z=0)
- hence (B/mu) > 1
R0 =
- B/mu
OR - B/sigma
R0
- the basic reproduction number
- the average number of secondary cases generated by a primary case in a totally susceptible population
- a fundamental measure of the transmission potential of a pathogen in a given setting
If you integrate out the dy/dt equation, what happens
you get a logistic
What is the equation for intrinsic growth rate
r = B - mu
What is the equation for carrying capacity
K = 1 - (1/R0)
Describe the SIR model of pathogenesis
- any individual in a population can be either Susceptible, Infected or Recovered (immune)
- individuals that are born are fed into S (b)
- individuals that die can leave at any stage (mu)
Individuals that are Susceptible and Infected are related by
lambda - the risk of infection
Those are Infected and Recovered are linked by
sigma - the rate of recovery
Describe measles virus
- hemagglutinin
- fusion protein
- SH protein
- matrix protein
- polymerase
- nucleoprotein
- phosphoprotein
Describe the dy/dt equation in light of the SIR model
dy/dt = By(1-z) - (sigma + mu) y
S
1 - z
Give the equation for dz/dt
By(1-z) - (mu x z)
Give the equation for dS/dt
bN - (lambda x S) - (mu x S)
Give the equation for dI/dt
lambda x S - (sigma x I) - (mu x I)
Give the equation for dR/dt
(sigma x I) - (mu x R)
Describe the similarities between pathogen-host dynamics and predator – prey systems
- cyclic (lag between consumption and resource renewal)
- getting eaten = becoming immune
- eating = infecting
- transmission = predator reproduction
Give some examples of viruses that broadly follow the SIR model (lifelong immunity with a short infectious period)
- measles
- mumps
- rubella
Give some examples of viruses that broadly follow the SI model (lifelong carriage)
- HIV
- herpesviruses
- syphilis
What is the aim of eradication?
reduce the average number of secondary cases generated by an index case to less than one
How is eradication achieved?
- p immunised must exceed the fraction immune at equilibrium (in the absence of vaccination)
- p > 1 - (1/R0)
p
proportion
Why is malaria so deadly?
it demonstrates antigenic variation and co-circulating strains
