1. Class 21: Spreading Phenomena PartI
Prof. Boleslaw Szymanski
Yong-Yeol Ahn and Alex Vespignani ;
Network Science: Epidemic Modeling 2015

2. Why is the spreading process important?
Epidemic spreading – Why?
Why is the spreading process important?
Network Science: Epidemic Modeling 2015

3. Epi + demos “Epidemic” Biological: Airborne diseases (flu, SARS, …)
Venereal diseases (HIV, …)
Other infectious diseases including some cancers (HPV, …)
Parasites (bedbugs, malaria, …)
Digital:
Computer viruses, worms
Mobile phone viruses
Conceptual/Intellectual:
Diffusion of innovations
Rumors
Memes
Business practices
Epi + demos
upon people

4. Biological: Notable Epidemic Outbreaks
The Great Plague
HIV
SARS
H1N1 flu
1918 Spanish flu

5. Epidemic spreading – Why does it matter now?
High population density
High mobility
 perfect conditions for epidemic spreading.
Airline figure: L. Hufnagel et al. PNAS 101, (2004)

6. Large population can provide the “fuel”
Separate, small population
(hunter-gatherer society, wild animals)
Connected, highly populated areas
(cities)
Human societies have “crowd diseases”, which are the consequences of large, interconnected populations (Measles, tuberculosis, smallpox, influenza, common cold, …)
Network Science: Epidemic Modeling 2015

7. 14th Century – The Great Plague
4 years from France to Sweden
Limited by the speed of human travel
The Black Death was one of the most devastating pandemics in human history, peaking in Europe between 1348 and It is widely thought to have been an outbreak of bubonic plague caused by the bacterium Yersinia pestis, an argument supported by recent forensic research, although this view has been challenged by a number of scholars. Thought to have started in China, it travelled along the Silk Road and had reached the Crimea by From there, probably carried by Oriental rat fleas residing on the black rats that were regular passengers on merchant ships, it spread throughout the Mediterranean and Europe.
The Black Death is estimated to have killed 30% – 60% of Europe's population,[1] reducing the world's population from an estimated 450 million to between 350 and 375 million in This has been seen as having created a series of religious, social and economic upheavals, which had profound effects on the course of European history. It took 150 years for Europe's population to recover.

8. 21st Century – SARS Source: World Health Organization
Severe acute respiratory syndrome (SARS; pronounced /ˈsɑrz/ sarz) is a respiratory disease in humans which is caused by the SARS coronavirus (SARS-CoV).[1] There was one near pandemic, between the months of November 2002 and July 2003, with 8,422 known infected cases and 916 confirmed human deaths[2] (a case-fatality rate of 9.6%) worldwide being listed in the World Health Organization's (WHO) 21 April 2004 concluding report.[3] Within a matter of weeks in early 2003, SARS spread from the Guangdong province of China to rapidly infect individuals in some 37 countries around the world.[4](WIKI, SARS)
Source: World Health Organization

9. Computer Viruses, Worms, Mobile Phone Viruses
Code Red Worm paralyzed many countries’ Internet
Why do we care about mobile phone viruses?
they are limited to SmartPhones, like iPhone, BlackBarry, Palm.
the SmartPhone market is increasing at 150% rate,  in a few years they will replace the regular mobile phones  we will have more computers in our hands, than on our desks.
I wonder, how many of you have experienced a mobile phone virus before? Hands up, please!
This is not because there are no viruses out there– in fact, in 2006 experts already collected close to 350 different mobile viruses.
if there are so many phone viruses out there, we have we not experienced mobile phone virus outbreaks in the past? This is what I want to answer in this talk.
The Code Red worm was a computer worm observed on the Internet on July 13, It attacked computers running Microsoft's IIS web server.
The Code Red worm was first discovered and researched by eEye Digital Security employees Marc Maiffret and Ryan Permeh. The worm was named the .ida "Code Red" worm because Code Red Mountain Dew was what they were drinking at the time, and because of the phrase "Hacked by Chinese!" with which the worm defaced websites.[1]
Although the worm had been released on July 13, the largest group of infected computers was seen on July 19, On this day, the number of infected hosts reached 359,000.[2][CODE RED, WIKI]
Hypponen M. Scientific American Nov (2006).

10. Diffusion of Innovation – The Adoption Curve
Late majority
Broadcast
Laggards
Contagion
Early majority
Innovators
Early adopters
Reference unknown

11. Spreading of Influence
Information Spreading

12. Epidemic spreading always implies network structure!
Epidemic Spreading – Network
Epidemic spreading always implies network structure!
Spreading happens only when the carries of the diseases/virus/idea are connected to each other.

13. Epidemic Spreading – Network
Why do we care about mobile phone viruses?
they are limited to SmartPhones, like iPhone, BlackBarry, Palm.
the SmartPhone market is increasing at 150% rate,  in a few years they will replace the regular mobile phones  we will have more computers in our hands, than on our desks.
I wonder, how many of you have experienced a mobile phone virus before? Hands up, please!
This is not because there are no viruses out there– in fact, in 2006 experts already collected close to 350 different mobile viruses.
if there are so many phone viruses out there, we have we not experienced mobile phone virus outbreaks in the past? This is what I want to answer in this talk.
Internet
The transportation network

14. Epidemic Spreading – Network
Why do we care about mobile phone viruses?
they are limited to SmartPhones, like iPhone, BlackBarry, Palm.
the SmartPhone market is increasing at 150% rate,  in a few years they will replace the regular mobile phones  we will have more computers in our hands, than on our desks.
I wonder, how many of you have experienced a mobile phone virus before? Hands up, please!
This is not because there are no viruses out there– in fact, in 2006 experts already collected close to 350 different mobile viruses.
if there are so many phone viruses out there, we have we not experienced mobile phone virus outbreaks in the past? This is what I want to answer in this talk.
The transportation network
Internet
L. Hufnagel et al. PNAS 101, (2004)

15. Types of Spreading Phenomena and Networks
Agent
Venereal disease
Sexual network
pathogens
Other infectious disease
Contact network, transport network
Rumor spreading
Communication network
Information, memes
Diffusion of innovation
Ideas
Internet worms
Internet
Malwares (binary strings)
Mobile phone virus
Social network / proximity network
Bedbugs
Hotel – traveler network
Malaria
Mosquito – Human network
Plasmodium
Network Science: Epidemic Modeling 2015

16. Epidemic Modeling (classical models)
Classical Models of Epidemics
Epidemic Modeling
(classical models)
Network Science: Epidemic Modeling 2015

17. S I R Classical Epidemic Models – Basic States Infection Removal
Recovery
Recovery
Susceptible
(healthy)
Infected
(sick)
Removed
(immune / dead)

18. S I R SIS Model: Common Cold Infection Removal Recovery Recovery
Susceptible
(healthy)
Infected
(sick)
Removed
(immune / dead)

19. S I R Example 2: Flu, SARS, Plague, … Infection Removal Recovery
Susceptible
(healthy)
Infected
(sick)
Removed
(immune / dead)

20. S I R Simplest Model: SI Infection Removal Recovery Recovery
Susceptible
(healthy)
Infected
(sick)
Removed
(immune / dead)

21. SI Model: Homogeneous Mixing (No network)
Each individual has β contacts with randomly chosen others individuals per unit time.
with
M. E. J. Newman, Networks: an introduction

22. SI Model: Dynamics Susceptible + Infected  more Infected I S
Logistic equation: a basic model of population growth.

23. SI model: the fraction infected increases until everyone is infected.
SI Model – Behavior
As i(t) 1.
If i(t) is small,
Fraction Infected i(t)
saturation
exponential
outbreak
Time (t)
SI model: the fraction infected increases until everyone is infected.

24. S I R SIS Model: Common Cold Infection Removal Recovery Recovery
Susceptible
(healthy)
Infected
(sick)
Removed
(immune / dead)

25. SIS model: fraction infected individuals saturates below 1.
Fraction Infected i(t)
Time (t)
Stationary state:
SIS model: fraction infected individuals saturates below 1.
“Epidemic threshold”

26. SIS Model: Epidemic Threshold and Basic Reproductive Number
On average, how many uninfected individuals will be infected by one infected individual?