# Using Simulated Annealing to Improve the Information Dissemination Network Structure of a Foreign Animal Disease Outbreak Response

James D. Pleuss, Jessica L. Heier Stamm and Jason D. Ellis

# Abstract

Communication is an integral part of emergency response, and improving the information dissemination network for crisis communication can save time, resources, and lives. In a foreign animal disease (FAD) outbreak, timeliness of detection and response are critical. An outbreak of foot-and-mouth disease, a particularly significant FAD, could cripple the agriculture economy. This research uses communication data from a FAD response exercise in Kansas to develop a reliable crisis communication network model, contributing a general method for creating an information dissemination network from empirical communication data. We then introduce a simulated annealing heuristic that identifies an alternative network structure that minimizes the time for information to reach all response participants. The resultant network structure reduces overall information transmission time by almost 90% and reveals actionable observations for improving FAD response communication. We find that not only can a crisis communication network be improved significantly, but also that the quantitative results support qualitative observations from early in the data extraction process. This paper adds original methods to the literature and opens the door for future quantitative work in the area of crisis communication and emergency response.

## Appendix I

### Network Model Example

Figure 10 shows an example network.

### Figure 10:

Diagram of Example Network; Label on Arc (i,j) is wij and Label on Node i is [wi, λimax]

Table 7 gives the probability matrix for the example network in Figure 10.

### Table 7:

Probability Matrix for Example Network.

P MatrixABCD
A00.40.60
B1000
C00.40.20.4
D0.600.40

To understand the informed time for a node and for the network, consider the following series of events using the example network in Figure 10. The information to be transmitted originates at node A, indicating that a member of A was the first to have this information and communicate it with someone else in the network. This means that λA = 1 at the start of the simulation while λB, λC, and λD are each 0. Because λAmax=2, node A is not yet informed. Suppose node A first transmits to node B. Information transmission is binary in nature, meaning one cannot partially transmit information. This makes λB = 1 and, becauseλBmax=1, node B becomes informed. The simulation continues until all nodes and, thus, the network, are informed.

## Appendix II

### Simulation Model Replications

The process for computing the appropriate number of simulation replications is based on (Devore 2016). To ensure with 95% confidence that the true average informed time is within 100 minutes of the observed average informed time from the simulation replications, an initial sample of 50 replications was taken. The required number of replications, r, comes from the following equation: r=(tα/2sB)2, where s is the sample standard deviation, tα/2 is the critical value of the student-t test, and B is the desired precision level (in our case 100). We found the required number of replications for each of the three injects to be 367.07, 292.88, and 327.72. Based on this information, we chose to perform 400 replications for each inject.

## Appendix III

### Simulation Model Validation

Table 8 shows the comparison for how long it took for nodes to be informed of a presumptive positive FMD in the actual exercise versus our simulation model. Comparing the exercise and simulation times of each row suggests that the simulation model is, indeed, representing this information flow in the network closely, particularly for the first seven nodes, where the times differ on average by less than 15 minutes. Additionally, the simulation replicates the sequence of the first three nodes perfectly, and the nine exercise nodes that received the information are represented in the first 13 nodes of the simulation.

### Table 8:

First Informed Times for Presumptive Positive FMD and Inject 3 across 400 Replications.

Number of Nodes First InformedNodeExercise Time (min)NodeSimulation Time (min)
1D0.00D0.00
2I0.00I25.78
3P0.00P41.51
4O54.00Q47.88
5G60.00B53.85
6N60.00R67.01
7F60.00G69.32
8K110.00F82.48
9H150.00L82.66
10H87.66
11K92.59
12O142.32
13N333.06
14J379.19
15C403.47
16A553.48
17E609.69
18M1029.17

The only other instance from the exercise with enough transmission documentation to analyze is when a bull with possible FMD is discovered in the Kansas State University College of Veterinary Medicine (L). This event most closely resembles inject 2 of the simulation where an individual producer (E) introduces information to the network. With this in mind, Table 9 shows the same comparison as the previous instance. All seven exercise nodes that received the information are represented within the first 11 nodes of the simulation. Also, the average difference in times for the individual nodes is less than 25 minutes. Thus, we conclude that the proposed simulation model is a valid representation of the crisis communication network from the exercise, and the remainder of the paper builds on this network simulation model.

### Table 9:

First Informed Times for Bull at KSU CVM and Inject 2 Across 400 Replications.

Number of Nodes First InformedNodeExercise Time (min)NodeSimulation Time (min)
1L0.00E0.00
2I0.00I42.54
3K108.00Q69.13
4G108.00B81.59
5B117.00G89.30
6R117.00L91.76
7H139.00R93.09
8F102.61
9K111.48
10P111.87
11H118.61
12O195.80
13D265.44
14J390.85
15N395.21
16M424.68
17C462.76
18A561.43

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Published Online: 2018-07-10

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