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Parasites and Disease
I. Definitions What is a parasite? What is a disease?
A. 1) A parasite is (almost always) an organism
2) A disease sis a set of symptoms in a host
B. Classification by life history
1) Macroparasites
(ex. Arthropods, flatworms, nematodes, annelids, fungi)
a. typically release reproductive products from the host
b. a few to many per host
c. parasite’s reproductive rate ~ to that of the host
d. the unit of study can be the parasite itself
e. studied growth rate is that of the parasite or parasite population
f. immunity not too common
2) Microparasites
(ex. bacteria, viruses, protozoans)
a. multiply within the host
b. reproductive rate much higher than the host
c. the usual unit of study is infected hosts
d. studied growth rate is the rate of appearance of new infections
e. immunity is an important life history factor for host and parasite
C. Transmission mode
1) Direct: From infected definitive host to infected definitive host
2) Vector: One or several intermediate hosts are involved
(definitive host is the host where parasite sexual reproduction takes place)
II. Epidemiology – the study of the rate of spread of infection
Growth rate studied is the rate of appearance of new infections
Basic question is whether net growth rate R0 is
= 1 no spread
< 1 disease spreads
< 1 disease disappears
A. Directly transmitted microparasite SIR model
Susceptible Infected Resistant
R0 = βS fL
Where:
S is the density of susceptible hosts
β is the transmission rate of the parasite
f is the fraction of hosts that survive long enough to become infective themselves
L is the length of life when it is invective
B. The dynamics of each of the compartments is represented by a differential equation:
Basic
dS/dt = - λSI
dI/dt =
λSI
dR/dt =
-νI
νI
more complete
dS/dt = (a -φN) [S + R + Iρ(1-e)] – bs + ξR – λ(I)
dI/dt = λ(I)S + I(α - φN)eρ – (α + b + ν)
dR/dt = νI – (b + ξ)R
Where:
a = host birth rate
b = natural host death rate
φ = density dependant reduction in host births
λ = rate at which susceptible individuals become infected by an infectious disease
e = proportion of infected females that produce infected offspring
ρ = reduction of fecundity of host individuals due to infection
ν = recovery rate of infected individuals
α = virulence
ξ = rate of loss of resistance
For the disease to persist, there must be a minimum threshold size of the host population Nt
Nt = (βfL)-1
So for example;
if L is large (host remains alive and infective a long time) R0 can be > 1 even if N is small
if β is large (high infection rate) R0 can be > 1 even if N is small
if f is large (survival of infected hosts is high) R0 can be > 1 even if N is small
Conversely, diseases with low rate of transmission, short duration of infection, high host
mortality are likely to require a very large host population to persist
C. Vector born diseases
R0 = β2 Nv/Nh fv fh Lv Lh
Why is transmission rate β squared? Infection passes to and from the host
Nv is density of vector population
Nh is density of host population
Nv/Nh functions as a ‘dilution’ parameter
f & L are as before but for vector and host separately
If R0 = 1 is the threshold for maintenance of the parasite in the host population then:
Nv/Nh = (β2 fv fh Lv Lh)-1
D. Macroparasites
R0 = (λ La fa) (β N Lv Ln)
The first term represents the reproductive contribution of the adult parasite
The second term represents the reproductive contribution of the infective stage(s)
λ = rate of egg production per adult
β = transmission rate
N = density of susceptible hosts
La = life expectancy of a mature parasite in the host
Li = life expectancy of the infective stage(s) outside the host
Fa = the proportion of parasites in the host that reach sexual maturity
Fi = the proportion of the transmissive stage(s) that become infective
Or for Macroparasites with indirect transmission
R0 = (λ1 La1 fa1) (β1 N1 L1v L1n) (λ2 La2 fa2) (β2 N2 L2v L2n) (λ3 La3 fa3) (β3 N3 L3v L3n) (etc.)
E. Plant parasites
DXTdt = Rc (XT-P) (1-XT)
Where
Rc = multiplication rate
XT = proportion of plants affected by lesions at time T
P = length of the latent period
So:
(XT-P) is the proportion of plants affected by infective lesions
(1-XT) is the proportion of the plant population susceptible to infection
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