Structure of Networks

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From the course by The Pennsylvania State University

Epidemics - the Dynamics of Infectious Diseases

571 оценки

The Pennsylvania State University

Epidemics - the Dynamics of Infectious Diseases

571 оценки

Not so long ago, it was almost guaranteed that you would die of an infectious disease. In fact, had you been born just 150 years ago, your chances of dying of an infectious disease before you've reached the tender age of 5 would have been extremely high. Since then, science has come a long way in understanding infectious diseases - what they are, how they spread, and how they can be prevented. But diseases like HIV/AIDS, Malaria, Tuberculosis, or the flu are still major killers worldwide, and novel emerging diseases are a constant threat to public health. In addition, the bugs are evolving. Antibiotics, our most potent weapon against bacterial infections, are losing their power because the bacteria are becoming resistant. In this course, we'll explore the major themes of infectious diseases dynamics. After we’ve covered the basics, we'll be looking at the dynamics of the flu, and why we're worried about flu pandemics. We'll be looking at the dynamics of childhood diseases such as measles and whooping cough, which were once considered almost eradicated, but are now making a comeback. We'll explore Malaria, and use it as a case study of the evolution of drug resistance. We'll even be looking at social networks - how diseases can spread from you to your friends to your friends' friends, and so on. And of course we’ll be talking about vaccination too. We’ll also be talking about how mobile phones, social media and crowdsourcing are revolutionizing disease surveillance, giving rise to a new field of digital epidemiology. And yes, we will be talking about Zombies - not human zombies, but zombie ants whose brains are hijacked by an infectious fungus. We're looking forward to having you join us for an exciting course!

From the lesson

Epidemiology

Where humans live and how they are connected to each other, have strong effects on how infectious diseases can spread. In this module, you will learn about some of the related key concepts of epidemiology. After looking at some fascinating history, we’ll learn about social networks as the ultimate “road map” on which diseases can travel and we’ll talk about how the structure of the network can influence disease dynamics. After that, we’ll cover three topics that all affect infectious disease epidemiology in dramatic ways: human transport systems, population density and so-called superspreaders - individuals who can spread a disease to dozens or even hundreds of other individuals. We’ll close by identifying what information is required for disease surveillance.

Roots of Epidemiology6:25

Social Networks5:45

Structure of Networks5:49

Superspreaders6:09

Meet the Instructors

Dr. Ottar N. Bjornstad
Professor of Entomology and Biology
Department of Biology
Dr. Rachel A. Smith
Associate Professor
Department of Communication Arts & Sciences and Human Development & Family Studies
Dr. Mary L. Poss
Professor of Biology
Department of Biology
Dr. David P. Hughes
Assistant Professor of Entomology and Biology
Department of Biology
Dr. Peter Hudson
Willaman Professor of Biology
Department of Biology
Dr. Matthew Ferrari
Assistant Professor of Biology
Department of Biology
Dr. Andrew Read
Alumni Professor in the Biological Sciences, and Professor of Entomology
Center for Infectious Disease Dynamics
Dr. Marcel Salathé
Assistant Professor of Biology
Department of Biology

Social networks are the roadmaps in which infectious diseases travel.

In these networks, people or hosts, more generally, are represented by nodes.

And potential disease transmission events are

represented by edges between the nodes.

If we know the structure of a network, we're much better

able to understand how the disease will spread on that network.

And how it can

best be controlled.

Large networks are very complex structures.

But we can reduce their complexity by looking

at the general structural properties of the network.

Among the most important is a property called the degree distribution.

The degree of the given node is the number of edges that this node has.

In a social

network then, the degree corresponds to the number of contacts that a person has.

More contacts translates into more disease transmission, which is

why the degree is an important measure on its own.

Now, we can count the number of contacts for each node, and then we

can take a look at the distribution of these degrees over the entire network.

Let's take a look

at a concrete example. This is a simple, rather small network.

It has 500 nodes and 2500 edges.

But it helps to illustrate the point.

First, we would count the number of edges that are

attached to each node, that's the degree of a node.

Then we would want to look at the degree distribution over the entire network.

For this particular network, the degree distribution looks like this.

As you can see, the average degree is 10.

The lowest degree is 8, and the highest degree is 13.

In order to understand why the degree distribution is important, we

need to understand how it affects the basic productive number R nought.

Imagine a node in our network that is infectious.

Let's say this is the first infected node in the network.

First, we need to know the probability of disease transmission per contact.

That's straightforward. It is simply the total time that the node

is infectious, L times the probability of disease transmission per unit time beta.

So the product of these two

numbers is the per contact transmission probability.

The more contacts you have therefore, the more individuals you would infect.

And this brings us right back to the degree distribution.

The average degree, which is the average number of contacts, is important because

a high average degree means that

there are many potential disease transmission possibilities.

Which will aid

the spread of the disease.

If everyone had the exact same number of contacts, we could write R nought

equals beta times L times K, where K is the average degree.

Again, beta times L is the probability of disease transmission per contact.

And we multiply this by the number of contacts K, which gives

us the number of infections caused by an infectious individual.

In reality, though, not everybody has the exact same number of contacts.

Some people have more contacts than average, others have fewer contacts.

In a distribution, the variance is a measure

of how far a distribution is spread out.

It turns out that when all else is equal, an increase

in the variance leads to an increase of R nought.

Mathematically, we can write the following.

Here, sigma squared is the variance of the degree distribution.

What this means is that the degree distribution can

actually have a very large effect on R nought.

Let me show you an example.

This network here is almost identical to

the one I showed before.

It has the same number of nodes, the

same number of edges, and the same average degree.

However, we can see that the degree distribution looks rather different.

This network's degree distribution clearly has

a higher variance than the other network.

It turns out that if we calculate the R naught for both of these networks, the R

naught of this high variance network is about four times

higher than the R naught of this low variance network.

That's a substantial change in R naught, and

as you know, a higher R-naught means more transmission.

More people getting sick, and control is going to be more difficult.

This is one of many reasons why understanding

the social network on which diseases spread is

so important.

I'd like to end by pointing out that

what we just learned, is important for control too.

Controlling the spread of disease means to reduce its R naught.

We can now understand that reducing the number of contacts or reducing the

variance in the degree distribution are both ways of reducing our node.

An efficient

strategy is to target nodes at very high degrees, and

to somehow protect them from getting and spreading the disease.

This strategy is efficient because it reduces both

the average degree, and the variance in a network.

And by doing so it reduces R naught.

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