Transition to extinction: Pandemics in a connected world

Figure 1: Host-pathgen model: hosts (green) pathogens (red) and empty space (black). This is also a predator-prey model with pathogens as predators and hosts as prey.

The video (Figure 1) shows a simple model of hosts and pathogens we have used to study evolutionary dynamics. In the animation, the green are hosts and red are pathogens. As pathogens infect hosts, they spread across the system. If you look closely, you will see that the red changes tint from time to time — that is the natural mutation of pathogens to become more or less aggressive.

Watch as one of the more aggressive—brighter red — strains rapidly expands. After a time it goes extinct leaving a black region. Why does it go extinct? The answer is that it spreads so rapidly that it kills the hosts around it. Without new hosts to infect it then dies out itself. That the rapidly spreading pathogens die out has important implications for evolutionary research which we have talked about elsewhere [1–7].

Figure 2: Flight map for an airline (KLM) some years ago.

In the research I want to discuss here, what we were interested in is the effect of adding long range transportation [8]. This includes natural means of dispersal as well as unintentional dispersal by humans, like adding airplane routes, which is being done by real world airlines (Figure 2).

When we introduce long range transportation into the model, the success of more aggressive strains changes. They can use the long range transportation to find new hosts and escape local extinction. Figure 3 shows that the more transportation routes introduced into the model, the more higher aggressive pathogens are able to survive and spread.

Figure 3: As we add more long range transportation links more aggressive pathogens survive. the types of pathogens change from those that are in the upper red to progressively the ones in the images toward the lower right. The lowest one on the right is a snapshot just before everything goes extinct.

As we add more long range transportation, there is a critical point at which pathogens become so aggressive that the entire host population dies. The pathogens die at the same time, but that is not exactly a consolation to the hosts. We call this the phase transition to extinction (Figure 4). With increasing levels of global transportation, human civilization may be approaching such a critical threshold.

Figure 4: The probability of survival makes a sharp transition (red line) from one to zero as we add more long range transportaion (horizontal axis). The right line (black) holds for different model parameters, so we need to study at what point the transition will take place for our world.

In the paper we wrote in 2006 about the dangers of global transportation for pathogen evolution and pandemics [8], we mentioned the risk from Ebola. Ebola is a horrendous disease that was present only in isolated villages in Africa. It was far away from the rest of the world only because of that isolation. Since Africa was developing, it was only a matter of time before it reached population centers and airports. While the model is about evolution, it is really about which pathogens will be found in a system that is highly connected, and Ebola can spread in a highly connected world.

The traditional approach to public health uses historical evidence analyzed statistically to assess the potential impacts of a disease. As a result, many were surprised by the spread of Ebola through West Africa in 2014. As the connectivity of the world increases, past experience is not a good guide to future events.

A key point about the phase transition to extinction is its suddenness. Even a system that seems stable, can be destabilized by a few more long-range connections, and connectivity is continuing to increase.

So how close are we to the tipping point? We don’t know but it would be good to find out before it happens.

While Ebola ravaged three countries in West Africa, it only resulted in a handful of cases outside that region. One possible reason is that many of the airlines that fly to west Africa stopped or reduced flights during the epidemic [9]. In the absence of a clear connection, public health authorities who downplayed the dangers of the epidemic spreading to the West might seem to be vindicated.

As with the choice of airlines to stop flying to west Africa, our analysis didn’t take into consideration how people respond to epidemics. It does tell us what the outcome will be unless we respond fast enough and well enough to stop the spread of future diseases, which may not be the same as the ones we saw in the past. As the world becomes more connected, the dangers increase.

Are people in western countries safe because of higher quality health systems? Countries like the U.S. have highly skewed networks of social interactions with some very highly connected individuals that can be “superspreaders.” The chances of such an individual becoming infected may be low but events like a mass outbreak pose a much greater risk if they do happen. If a sick food service worker in an airport infects 100 passengers, or a contagion event happens in mass transportation, an outbreak could very well prove unstoppable.

Watch this mock video of a pathogen spreading globally through land and air transportation. Long range transportation will continue to pose a threat of pandemic if its impacts cannot be contained.

[1] E. M. Rauch, H. Sayama, Y. Bar-Yam, Dynamics and genealogy of strains in spatially extended host pathogen models, J Theor Biol 221, 655–664 (2003).

[2] E. Rauch, H. Sayama, Y. Bar-Yam, Relationship between measures of fitness and time scale in evolution, Phys Rev Lett 88, 228101 (2002).

[3] E. M. Rauch, M. A. M. de Aguiar, Y. Bar-Yam, Mean field approximation to a spatial host-pathogen model, Phys. Rev. E 67, 047102 (2003).

[4] M. A. M. de Aguiar, E. M. Rauch, Y. Bar-Yam, Invasion and extinction in the mean field approximation for a spatial host-pathogen model, Journal of Statistical Physics 114, 1417–1451 (2004).

[5] J. K. Werfel and Y. Bar-Yam, The evolution of reproductive restraint through social communication. PNAS 101, 11019–11024 (2004).

[6] B.C. Stacey, A. Gros, Y. Bar-Yam, Beyond the Mean Field in Host-Pathogen Spatial Ecology. arXiv:1110.3845 (2011).

[7] J. Werfel, D.E. Ingber, Y. Bar-Yam, Programed death is favored by natural selection in spatial systems. Phys. Rev. Lett. 114, 238103 (2015) doi: 10.1103/PhysRevLett.114.238103

[8] E.M. Rauch and Y Bar-Yam, Long-Range Interaction and Evolutionary Stability in a Predator-Prey System. Physical Review E 73, 020903 (2006).

[9] e.g. A. Petroff, Airlines cancel flights over Ebola fears, CNN (August 6, 2014)