Lecture 11

Chapter 9: Host-Parasite Interactions

9.1 : Host-parasite interactions

Historical Perspective:

Theory of Microbes (1870s) Epidemiological models 1900s By 1920s models noted the role of population density in spread of disease - must reach a critical number for an epidemic to occur Medical epidemiology models 1950s Ecologists became in tune 1970s onward and now an active area of research (1) macroparasites Focus on (2) microparasite- host interactions (virus & bacteria) (3) parasitoid – host interactions (Chapter 10)

Macroparasite Background

Ex. Intestinal worms

Cause chronic, persistent infections (ex., malarial parasite)

Disease severity is dependent on number of parasites within host.

Number of macroparasites and their diversity increase with the age of vertebrate or invertebrate host increases

Average N. American mammal has 369 macroparasites of 3 different species! (Dobson et al. 1992)

Schistosoma mansoni story

Must find vert. Host w/in 48 hrs 4-7 wks

& asex repro

6-12 wks to mature & sex repro.

Microparasite Background

SIR Model

– Classifies hosts as susceptible (S), infected (I), or recovered (R)

MSEIR Model:

- individuals born with passive immunity (M)

- over time they loose immunity and become susceptible (S)

- individuals exposed to disease (E)

- individuals exposed join the infected group (I)

- of those that are infected survive become the recovered (R) group

9.2 Factors affecting microparasite population biology

Nokes (1992)

Three main factors influence interaction between host & microparasite:

(1) course of infection in host (latent and infectious periods)

(2) mode of transmission between hosts (vertical vs. horizontal and direct vs. indirect )

(3) behavior and demography of host (popln. size and density and close contact and sexual activity)

9.3 Modeling host-microparasite interactions

SIR model: N = total host population density

S = susceptible host density

I = infected host density

R = recovered (immune) host density

b = host birth rate

m = natural host mortality rate unrelated to disease

α = disease induced mortality

β = transmission rate from one host to another host

v = recovery rate (or per capita rate of passage from infected (I) to recovered (R) class = usually inverse of avg. infection period

γ = rate that recovered (R) indiv. loose their immunity ~ rate individuals return to susceptible (S) class from the R class.

Rate of transmission = βSI ~ called the “law of mass action” (Nokes 1992)

The total popln, N = S + I + R

9.3 Modeling host-microparasite interactions

SIR model:

Birth rate = bN

Rate recovered indiv loose immunity = γ R

Mortality of host NOT due to disease = mS

Mortality due to conversion of indiv. From S to R = βSI

Growth rate of susceptible class w/ each written as differential equation:

dS/dt = bN – mS - βSI + γ R eq 9.2

Growth rate of infected class:

dI/dt = βSI – (m + α + v) I eq 9.3

Growth rate of recovered class:

dR/dt = vI – mR - γ R eq. 9.4

9.3 Modeling host-microparasite interactions

SIR model:

Growth rate of susceptible class:

dS/dt = bN – mS - βSI + γ R eq 9.2

Growth rate of infected class:

dI/dt = βSI – (m + α + v) I eq 9.3

Growth rate of recovered class:

dR/dt = vI – mR - γ R eq. 9.4

Replace (b-m) by r (intrinsic rate of increase)

Growth of popln is reduced by “natural” death rate, m & disease (αI)

dN/dt = bN – mN - αI = rN – αI eq. 9.5

9.4 Dynamics of Disease

Rate of spread of disease:

Dependent on number of infected individuals must remain constant or increase

dI/dt > 0, Since dI/dt = βSI – (m + α + v) I

βSI - (m + α + v) I > 0 eq 9.6

βS - (m + α + v) > 0 eq 9.7

(m + α + v) are ALL time dependent and the inverse of (m + α + v) refers to length of infectious period, D

βS-1/D > 0 and βSD > 1 eq. 9.8

βSD = R0 (Basic Reproductive Number (BRN): R0 = βSD > 1 eq 9.9

9.4 Dynamics of Disease

Rate of spread of disease:

Define βSD = R0 = Basic Reproductive Number of disease (BRN)

R0 = βSD > 1 eq 9.9

R0 = mean number of new infections caused by a single individual

If R0 > 1 then dI>0 and incidence of disease (dI) will increase

If R0 < 1 then spread of disease ~ epidemic fails

R0 is directly proportional to the rate an infection spreads (βS)

9.4 Dynamics of Disease

Rate of spread of disease:

R0 is directly proportional to the rate an infection spreads (βS)

and is also influenced by D, length of infection period.

ST = minimum size of susceptible host popln for an epidemic to occur

Thus for a disease to spread it needs a dense popln of hosts!

Three criteria to help gauge disease 1) Vector abundance

2) Feeding focus

3) Vector longevity

To have an epidemic βND > 1 and minimum size of epidemic = N > 1/βD

R0 = S/ST eq. 9.12

Density of susceptible hosts > ST, then R0>1 and the infection spreads!

9.4 Dynamics of Disease

Rate of spread of disease:

Table 9.1 Measles cases reported by month in N Am. Cities 1921-1940

Table 9.2 Effect of popln size on mean age of infection for child hood diseases.

Table 9.3 Mean age of infection in England and Wales 1950-1955

Tendency of host-parasite (and predator-prey) interactions to exhibit oscillations is a natural process in principles of popln ecology (Turchin 2001)

9.5 Immunization

Goal – to reduce number of susceptible individuals within a population.

By defn this reduces the net reproductive rate of disease (BRN) to <1

Recall ST = 1/D where D = average infection period

= 1/ β where β = rate of infection

Thus high rate of infection and/or long course of disease makes effective immunizations difficult. New reproductive parameter is R*0

R*0 = S/ST = 1 = (1-p) R0

Immunized fraction of popln = p and disease will be eliminated when proportion immunized (p) must be > 1-1/R0

p = 1-1/R0 eq. 9.15

Table 9.4 Estimated fraction needed for successful immunization against diseases in New York State

9.6 Endangered metapoplns and disease

Role of dispersal or gene flow with respect to disease transmission

Hess (1996) negative impact of migrations w/r to disease transmission

Gog et al. (2002) most of infections threatening wild life are not caused by migration but spillover from other abundant hosts sympatric within a given habitat.

S = proportion of susceptible host patches (host patches w/ no disease)

I = proportion of infected patches (host patches & disease present)

xs, xI = extinction rates

Ψ = migration rate between infected and susceptible patches

δ = infected disperser arrives at susceptible patch and its probability of infecting resident population, δ

9.6 Endangered metapopulations & disease

S = proportion of susceptible host patches (host patches w/ no disease

I = proportion of infected patches (host patches and disease present)

xs, xI = extinction rates

Ψ = migration rate between infected and susceptible patches

δ = infected disperser arrives at susceptible patch & its probability of infecting resident popln, δ,

THEN: Infection spreads at a rate Ψ δIS

Gog = Hess, added another parameter, g

g = infection rate from outside source

Such that if g =0 or very small see Fig. 9.1 a

if g = a larger value see Fig. 9.1 b

Overall concluded corridors between suitable habitats most likely benefit metapopulation persistence.

9.7 Social Parasites

Definition = parasites that reduce fitness by its behavior

Includes brood or nest parasites

Cowbird

Cuckoo birds

Mafia Hypothesis

Slave making ants

Highlights: Host-Parasite Interactions

• Factors affecting microparasite population biology

• Modeling host–microparasite interactions

• Dynamics of the disease

• Endangered metapopulations and disease

• Social parasites