Epidemiology

population biology and dynamics of human diseases (infectious and non-infectious)

For our purposes, population dynamics of ALL infectious disease

Epidemiology's Goal:

To FORECAST and PREVENT disease-induced mortality and morbidity at the population level

Need to understand mechanisms underlying disease patterns

Pathogen dynamics

Changes in abundance (and effects) of pathogens through space and time

Example: Two Saiga die-offs

Event 1: 2015 calving season die-off

Event 2: transmission of

Peste des petits ruminants

(on-going)

Calving season die-off in Kazakhstan

Mortalities up to 100% of herds
REALLY fast (~three weeks)
Distinct timing in each herd

Pasteurella multocida

PPR in Mongolia

Sustained poor recruitment
Smaller die-offs
Along migration coorridor

Peste des petits ruminants

Example: Two Saiga die-offs

Event 1: 2015 calving season die-off

Event 2: transmission of

Peste des petits ruminants

(on-going)

Toxin interacting with commensal

Invasion of an emerging agent

Parasite dynamics

Changes in abundance (and effects) of parasites through space and time

PPR

Pasteurella multocida

(top down/bottom up figure!!)

Definitions

Epidemic: rapid rise in the prevalence of infection [to humans]

Epidemic curve: Time series of infected cases through time

Epidemic curve example

Phocine Distemper Virus in Harbour Seals

Klepac et al. 2008 PRSB

Estimated proportion of Harbour Seal populations which died during 1988 Epidemic

Definitions

Prevalence: proportion of host population infected or showing disease symptoms

Incidence: rate of new cases or infections

Percent seropositive: % of population showing acquired immunity (usually through some antibody-based metric)

Infectious period: Time when infected individuals can transmit pathogen to susceptibles (may not be associated with symptoms

Latent period: time from point of infection to shedding

Incubation period: time from infection to appearance of symptoms

Key drivers

Pathogen

Host

Environment

Individual level

Population level

Pathogen

Host

Environment

Pathogen

Host

Environment

Pathogen features

Pathogenicity: pathogen's ability to cause disease in the host

Virulence: magnitude of disease caused

Environmental persistence: ability of pathogen to survive outside the host

Host features

Immunity: host's ability to combat infection or disease due to presence of antibodies or other activated immune cells

Behavior: how do hosts move and interact with one another

Environmental context

Determines pathogen growth/survival

Determines host aggregation

Determines host susceptiblity

Pathogen

Host

Environment

Tropism

Immune efficacy

Environmental persistence

Immunopathology

Host

condition

Host

movements

Plasticity

Evolutionary potential

Epidemiological models

Individual level

Population level

Pathogen

Host

Environment

Pathogen

Host

Environment

Individual level

Population level

Pathogen

Host

Environment

Pathogen

Host

Environment

Pathogen

Host

\Delta \text{Host} \sim f(\text{Pathogen})

\Delta \text{Host} \sim f(\text{Pathogen})

\Delta \text{Pathogen} \sim f(\text{Host})

\Delta \text{Pathogen} \sim f(\text{Host})

Two Useful Comparisons

Pathogens as tiny predators

Hosts as islands

Pathogens as tiny predators

MacLulich, 1937

Some diseases also cycle

No vaccine

Vaccine

Predator-prey models

Prey

Predator

Predator deaths

Prey

births

Prey sparks predator growth

Predators kill prey

States

1. Prey pop size ("Prey")

2. Predator pop size ("Predator")

Transitions

1. Prey pop grows naturally

2. Prey sparks predator pop growth

3. Predator kills pres

Predator-prey models

\frac{d\text{Prey }}{dt} = \alpha\text{ Prey} - \beta (\text{Prey}\times \text{Pred})

\frac{d\text{Prey }}{dt} = \alpha\text{ Prey} - \beta (\text{Prey}\times \text{Pred})

\frac{d\text{Pred}}{dt} = \delta( \text{Prey}\times \text{Pred}) - \gamma \text{Pred }

\frac{d\text{Pred}}{dt} = \delta( \text{Prey}\times \text{Pred}) - \gamma \text{Pred }

Prey

Predator

Predator deaths

Prey

births

Prey sparks predator growth

Predators kill prey

States

1. Prey pop size ("Prey")

2. Predator pop size ("Predator")

Transitions

1. Prey pop grows naturally

2. Prey sparks predator pop growth

3. Predator kills pres

States

"changes in the"

Transitions

Hosts as "islands"

Insular (or "island") biogeography

Focal island

Immigration

Island 2

Island 3

Local pop growth;

Local extinction

Emigration

Island biogeography

2

3

1

States

Population sizes on each island

Transitions

1. Local population growth

2. Immigration

3. Emigration

4. Local extinction

\frac{dI_{1}}{dt} = b(I_{1}) +\text{Imm}(I_{2}+I_{3})-\text{Em}(I_{1})-\delta(I_{1})

\frac{dI_{1}}{dt} = b(I_{1}) +\text{Imm}(I_{2}+I_{3})-\text{Em}(I_{1})-\delta(I_{1})

\frac{dI_{2}}{dt} = b(I_{2}) +\text{Imm}(I_{1}+I_{3})-\text{Em}(I_{2})-\delta(I_{2})

\frac{dI_{2}}{dt} = b(I_{2}) +\text{Imm}(I_{1}+I_{3})-\text{Em}(I_{2})-\delta(I_{2})

\frac{dI_{3}}{dt} = b(I_{3}) +\text{Imm}(I_{1}+I_{2})-\text{Em}(I_{3})-\delta(I_{3})

\frac{dI_{3}}{dt} = b(I_{3}) +\text{Imm}(I_{1}+I_{2})-\text{Em}(I_{3})-\delta(I_{3})

States

Transitions

(local births)

(Immigration from elsewhere)

(emigration from here)

(local deaths)

Force of infection and clearance

2

3

1

Force of infection

Clearance

Infected hosts are islands of tiny "predators" for susceptible "prey" host islands

Contact

Removal of host

Pathogen clearance

2

3

1

Susceptible

Infectious

Recovered

Host states

requires

"contact"

between

S and I

Disease-induced mortalities

Recovery

\frac{dS}{dt} = \nu - \beta SI

\frac{dS}{dt} = \nu - \beta SI

\frac{dI}{dt} = \beta SI - \gamma I - \alpha I

\frac{dI}{dt} = \beta SI - \gamma I - \alpha I

\frac{dR}{dt} = \gamma I

\frac{dR}{dt} = \gamma I

States

Transitions

1. Susceptible

2. Infectious

3. Recovered

1. Transmission from I to S

2. Disease-induced mortality

3. Recovery

Births

(\nu)

(\nu)

(\beta SI)

(\beta SI)

(\alpha)

(\alpha)

(\gamma)

(\gamma)

Comparing disease systems

S

I

R

Comparison is important.

S

I

R

Axes for comparison

Transmission vs. Treatment

Measles

S

I

R

2. Completely immunizing

3. Consistent infectious period

4. All people without history of infection are susceptible

No vaccine

Vaccine

5. Model validated through natural experiment

1. Droplet transmission

Measles vs. HIV

HIV

Measles vs. HIV

Mode of transmission

Sexual contacts

Infectious period/Exerted force

Recovery/ Acquired immunity

Does not depend on pop. density

Higher pop. density = more contacts

Density-dependent ("DD") transmission

Frequency-dependent ("FD") transmission

vs.

Aerosolized droplets

S

I

R

S

I

Measles

HIV

Measles/HIV vs.

Malaria

Plasmodium tree,

Rutledge et al. Nature, 2017

Anopheles

Plasmodium falciparum

Plasmodium vivax

Measles/HIV vs. Malaria

Vectors!

Mode of transmission

Pathogen's life-history

Multiple relevant strains/Species

Environmental constraints

S

I

R

Measles

S

I

R

Malaria

(Vertebrate)

S

I

(Vector)

Measles vs.

Chronic Wasting Disease or Anthrax

Chronic Wasting Disease

Anthrax (Bacillus anthracis)

Ganz et al. PLoS NTD 2014

Measles vs. CWD or Anthrax

Environmental perisistence

S

I

R

Measles

S

I

R

Environmental persistence

E

Individual hosts

Spatial process

Measles vs.

Hendravirus in Flying Foxes

Hendra Virus

Plowright et al. PRSB 2011

Plowright et al. PRSB 2014

Measles vs. Hendra Virus in flying foxes

Plowright et al. PNTD 2016

Chronicity / Latency

S

I

R

Measles

days post-infection

pathogen load

Hendra

Measles vs.
Avian influenza

Avian influenza

Avian influenza: Drift and Shift

Holmes & Grenfell, PLoS Comp Biol, 2009

Antigenic DRIFT

Same hemagglutinin,

neurmidase

Antigenic SHIFT

Recombine hemagglutinins, neurimidases

Measles vs. Avian influenza

Evolutionary dynamics

S

I

R

Measles

S

I

S1

Avian influenza

Building conceptual models

1. Epizootic Hemorrhagic Disease / Bluetongue

2. Contagious Bovine Pleuropneumonia

3. Malignant Catarrhal Fever

4. West Nile Virus

5. Lyme disease

Identify key STATES and TRANSITIONS for each system

Quick intro to

Disease Ecology

Epidemiology

Epidemiology's Goal:

Pathogen dynamics

Example: Two Saiga die-offs

Calving season die-off in Kazakhstan

PPR in Mongolia

Example: Two Saiga die-offs

Parasite dynamics

Definitions

Definitions

Key drivers

Pathogen features

Host features

Environmental context

Epidemiological models

Two Useful Comparisons

Pathogens as tiny predators

Hosts as islands

Pathogens as tiny predators

Predator-prey models

Predator-prey models

Hosts as "islands"

Insular (or "island") biogeography

Island biogeography

Force of infection and clearance

Infected hosts are islands of tiny "predators" for susceptible "prey" host islands

Comparing disease systems

Comparison is important.

Axes for comparison

Transmission vs. Treatment

Measles

Measles vs. HIV

HIV

Measles vs. HIV

Measles/HIV vs.

Malaria

Malaria

Measles/HIV vs. Malaria

Measles vs.

Chronic Wasting Disease or Anthrax

Chronic Wasting Disease

Anthrax (Bacillus anthracis)

Measles vs. CWD or Anthrax

Measles vs.

Hendravirus in Flying Foxes

Measles vs. Avian influenza

Avian influenza

Avian influenza: Drift and Shift

Measles vs. Avian influenza

Building conceptual models

Measles vs.
Avian influenza