Resource allocation during emerging diseases

The allocation of resources, e.g. trained personnel and medical facilities as a measure of epidemic containment of emerging and recurrent diseases is an important component in international public health policy. However, because outbreaks affect different countries in different ways and outbreak associated risks are difficult to estimated because nations are interconnected in a complex way, optimal resource allocation is difficult to compute in a systematic manner. Often policies are still based on a national and regional political perspective that is no longer valid in the 21st century.

In this project we approach this problem in a systematic way. The model integrates two theoretic components: network theory and game theory. The foundation of the model is a network that represents the connectivity between countries which are nodes in the network. Link weights in the network represent the strength of connectivity between countries, e.g. the amount of people that travel between countries can be used as a proxy for this effective coupling between countries because traffic correlates with the propensity of disease spread between nodes. Each node is also considered a “player” in a game theoretic setup and each node can have an infectious state, representing the fact that an outbreak may or may not have occurred in the respective node.

Game theory is used to describe the decision-making. We define a cost function, which is minimized by the players. Two sources contribute to the cost: the resources allocated for disease prevention (investment) and expected cost of a local disease outbreak. The specific distribution of resources across the nodes of the network by a node i is called strategy of i. The choice of a strategy is only driven by self-interest, minimizing an individual node’s cost with no concern for other players.

We are interested inthe decision of the players, not in an optimal allocation enforced by a global entity. The key question here is whether optimal selfish strategies are those than allocate resources to other nodes, e.g. those that suffer from an outbreak or those that are in the immediate neighborhood of such nodes. It this is the case then this is clear evidence that self-interest is equivalent to investment in others.

By simulating the allocation process one can observe a variety of effects on the network. Even if no altruism is included in the decision-making, a fraction of nodes is investing most of the resources to other nodes, specifically to those that are affected by a disease.
Show Result

You can interact with the above network to see different states of the system when different nodes are infected. Double click the nodes to infect them (at the moment up to two infected nodes are available). Orange shading indicates infected nodes. Press 'Show result' to see how the strategies are distributed across the nodes: red - investment in the red infected, blue - investment in the blue infected, green - investment in self, light gray - no investment, dark grey - other strategy. To un-infect the nodes double click on them again or use the 'Reset' button

From the network above it can be seen that the proximity of the node to an infected increases its tendency to invest in it, while nodes at equal distance to both tend to use the resources to raise their own preparedness.

With the framework described above it is possible to study the influence of system parameters, network topology and position of the player on the network on the behavior of the agents. We intend to refine the model to account for more aspects, which influence the process in the real world.