Epidemiological Modeling of Infectious Diseases

Why do we use epidemiological models for studying

infectious disease dynamics?

The Global Infectious Disease burden

1) The increasing threat of infectious diseases: emergin infectious diseases (SARA, Middle East Respiratory Syndrome, Avian influenza, Swine flu, Zika virus

2) Drug Resistance

3) Vaccine Refusals/Sacres

Understanding infectious disease is a multifaceted approach - what are a few different facets to understanding infectious disease?

Medicine, genomics, microbiology, immunology, vaccine and drugs

What is an infectious disease model?

a set of equations describing transmission of a pathogen in a population with an attempt to capture key processes, ignoring unnecessary detail

Why do we need mathematical models for studying infectious disease? In other words - what do these models help us understand?

1) The dynamics of infectious diseases are complex: - rise and fall in number of cases

- Oscillations (seasonality of disease prevalence)

2) Non-linearities:

- small changes in input can produce large changes in output

- Herd/indirect effects of disease spread and control (e.g herd immunity effect)

*What three type of questions can mathematical infectious disease models help us answer?

1) To help us Understand transmission dynamics

2) Assessing control strategies

3) Predict future course

*The following are all examples of what type of general question an infectious disease model might help us answer?

- Who are the age-groups contribute the most to transmission?

- Where are the hotspots?

- Highlight gaps in knowledge, data needs, etc

What are the transmission dynamics/what affects/determines transmission?

*The following are all examples of what type of general question an infectious disease model might help us answer?

- What fraction of the population must be immunized to prevent an outbreak?

- Limited vaccine supply, how should it be distributed?

- What should be the level and duration of travel restriction, school closures?

What control strategies work/should be put in place?

*The following are all examples of what type of general question an infectious disease model might help us answer?

- How many cases do we expect next week?

- Are we approaching the peak of an outbreak?

What is the future course of this disease?

*What are three fundamental features of an infectious disease model?

1) Accuracy

2) Transparency

3) Flexibility

*What is meant by the accuracy of a model?

• The ability of the model to capture observed patterns (qualitative or quantitative?) and make predictions

• Increases with model complexity

*The accuracy of a model ___________ with the complexity of the model.

increases

(complex - taking into account all the things in reality)

*What is meant by the transparency of a model?

• Ability to understand the components of a model

*The transparency of a model ____________ with the complexity of the model.

decreases

*What is meant by the flexibility of a model?

• How easily the model can be adapted to new scenarios

*The flexibility of a model _____________ the more complex a model is.

decreases

(more components --> more tailored to one disease/scenario than another)

*What two steps are required in building a mathematical model for understanding infectious disease?

1. Define health states

2. Determine transition rules

*What's the difference between clinical and infection status?

clinical status: healthy, incubating, disease

infection status: susceptible, exposed, infectious, recovered/immune

Clinical status is based on what individual is like clinically, whereas infection status is based on ability to transmit/be infected with pathogen

*What are some (four) health states that are used in a mathematical model for understanding infectious disease?

Susceptible, Exposed, Infectious,

Removed

*What is a Susceptible health state?/who are these people?

naïve individuals, they are susceptible to disease

*What is an Exposed health state?/who are these people?

they are infected by pathogen, but not yet infectious

*What is an Infectious health state?/who are these people?

they are able to transmit pathogen to others

*What is a Removed health status?/who are these people?

immune individuals that don't contribute to further transmission of pathogen

Transmission is a product of what three things (in an SIR model)?

a function of # of contacts, the prevalence of disease and multiplied by ______

What is the threshold phenomenon?

it is the minimal number of infected individuals that would predict whether an epidemic would occur

What is R(0)?

The average number of secondary infectious cases resulting from the introduction of a single infectious case into a totally susceptible population

What three things does the reproduction number, R(0) depend on?

1. The number of contacts a person has per time, c

2. The probability of transmission given contact, 𝜗

3. The duration of infectiousness, D

If R(0) is less than 1, the number of cases __________

If R(0) is greater than 1, the number of cases __________

decreases

increases

The __________ the reproductive number the more effective the intervention must be to reduce the spread of the pathogen

higher

How do we know how much of the population should be vaccinated in order to prevent an epidemic, concerning reproductive number? (review from other lecture)

1- (1/R(0))