Akureyri Disease: SIR Model Analysis
Introduction
1.1 History of Disease
Akureyri disease spread in Iceland from the year 1948; it has also been called Icelandic disease in international theses. It was in the same group as myalgic encephalomyelitis (ME), which is chronic fatigue syndrome (Sigurdsson B. S., 1950).
Akureyri disease mostly affected a certain group of people, that was primarily younger people and primarily women. There were many young students in Menntaskólinn á Akureyri (the College of Akureyri) who got infected. The population in Akureyri at that time was 6900 persons, and 7% of them got infected, or about 465 people. Of those 465 people, only 15% fully recovered, and 25% had bad symptoms their whole lives. Even those who eventually recovered were ill for several months (Sigurdsson B. &., 1956).
The symptoms people got were a fever that lasted a long time, but never went above 38 degrees Celsius. People experienced bone and joint pains and muscle soreness. Headaches and stiffness in the neck were also some of the symptoms. All these symptoms are common to normal sickness, but they discovered it was a different sickness than a normal fever when other symptoms appeared, such as mental health issues like stress and anxiety. People got powerless in the body and sometimes only in one side of their body, like in one leg, and then ended up paralyzed. These symptoms indicated that the disease primarily targeted the nervous system. Initially, however, many patients were not taken seriously and were told that their symptoms were psychological rather than physical. This outbreak occurred many years later compared to other similar epidemics, often compared to epidemic neuromyasthenia (Parish, 1978).
The first case was diagnosed not far away from Akureyri in 1948. Akureyri is a small town in northern Iceland, with a population of 6900 people at that time. In the end, 7% of the town got infected. It spread in many other small towns around Akureyri, but the majority of cases were in Akureyri. The peak of the outbreak was in the winter of 1948-1949. However, there were no signs of the disease in Akureyri after 1949, and no cases anywhere in Iceland after 1955 (Bergmann, 2006).
Percent: How many People:
Full recovery: 15% 70 People
Mostly recovery: 60% 279 People
Little recovery: 25% 116 People
Table 1. Recovery outcomes in Akureyri
Percent: How many People:
Akureyri: 95% 465 People
Other: 5% 23 People
Table 2. Distribution of cases across Iceland
1.2 History of SIR
The founders of SIR models, McKendrick and Kermack, are from Scotland. In 1927, they published their influential paper “A Contribution to the Mathematical Theory of Epidemics.”. There, they introduced an epidemiological model study of disease and described the dynamics of the disease spread based on differential equations. This was the first formal study of its kind, and after that, many other models have been discovered based on that. In this study, we are using it on Akureyri disease (Kermack, 1927).
SIR models divide a population into three classes: S-susceptible, I-infectious, and R-recovered. The main idea is to analyze how people transition from one class to another and how long they remain in each state (Hethcote, 2000). That is why it is good to use the gamma distribution. That was the first study about the SIR model. In this project, we use the SIR model. It is important to see how outbreaks can affect the public and see what is driving them, and try to understand them.
1.3 Motivation
There is not a lot of information out there about this disease. During the outbreak, many patients were not taken seriously and were often treated poorly. Understanding better what happened in the past helps us prepare more for the future. So now that we know more about how the disease spreads, we can be more prepared and respond faster and more effectively if it happens again.
2. Method
2.1 Model
The SIR model in mathematical language could be described by a system of ordinary differential equations, where the population is divided into three classes: susceptible (S), infectious (I), and recovered (R). In this case, we assume that we don’t have any changes in population, so no births or deaths.
These equations describe the rates at which individuals move between classes, where β is the transmission rate and γ is the recovery rate.
2.2 Python and Code Description
In this project, we described the SIR model using Python (Python Software Foundation, 2025). The code defines the key parameters: the transmission rate (β), the recovery rate (γ), and the total population (N). Initial conditions are set for the numbers of susceptible, infectious, and recovered individuals. Using a time loop, the program updates these values at each time step based on the differential equations of the SIR model. Finally, the code produces a plot showing the changes in the three groups—susceptible, infectious, and recovered—over time, providing a visualization of the epidemic dynamics. The code could be found in the Appendix. In Figure 1, you can see a visualization of the SIR model with a transmission rate of 0.001, with a recovery rate of 0.1, with a total population of 1000, and a total time of 100 days.
Figure 1. Standard SIR Model.
2.3 Parameter Variation in SIR Model
SIR models are used to study how diseases spread through a population. The model divides people into three groups: S for susceptible individuals, I for infectious individuals, and R for recovered individuals.
By adjusting the model’s parameters, we can explore how changes affect the course of an epidemic (Kermack, 1927). For example, increasing β (the transmission rate) means individuals are more likely to become infected, so the disease spreads more quickly. If β is smaller, the spread is slower, and fewer people are infected. Similarly, γ (the recovery rate) determines how quickly infected individuals recover. A larger γ means faster recovery, while a smaller γ means people remain ill for a longer period (Hethcote, 2000).
By varying these parameters, we can better understand how the Akureyri disease outbreak might have unfolded and how it affected the community at that time. In Figure 2, you can see a visualization of the SIR model with a transmission rate of = 0.00003188405, with a recovery rate of 0.143, with a total population of 6900, and a total simulation time of 180 days.
3. Results and Discussion
Figure 2. SIR Model for Akureyri disease.
The results from the SIR model show that the Akureyri disease spread quickly in a small area of Akureyri, with only 6900 people living there. However, the number of cases decreased quickly again, and people recovered fast. As seen in Figure 2, the number of infected increased rapidly. This matches historical information about the fact that most people got sick in the winter of 1948-1949, and then it decreased afterwards.
Not much was known about this disease at the time it spread. Some patients were not taken seriously, and none were said to have died from it, but old memorial articles say that people may have died from it, although it was shameful to admit. (Pétursson, 1996).
This SIR model gives us insight into how the disease developed, though the model is a simplification. The model cannot show long-term effects and nerve damage that some of the patients got (Sigurdsson B. S., 1950), but it will help us to understand how diseases can spread. By using modern mathematics models on historical data, we can learn from the past and be prepared for the future.
Appendix.
import numpy as np
import matplotlib.pyplot as plt
# Parameters
beta = 0.001 # transmission rate
gamma = 0.1 # recovery rate
N = 1000 # total population
# Initial conditions
I0 = 1
R0 = 0
S0 = N-I0-R0
# Time settings
T = 100 # total simulation time
dt = 0.1 # time step
steps = int(T/dt)
# Make arrays
S = [S0]
I = [I0]
R = [R0]
t = [0]
# Start simulation
n = 0
while n < steps:
current_S = S[-1]
current_I = I[-1]
current_R = R[-1]
current_t = t[-1]
# Compute derivatives
dS = -beta * current_S * current_I
dI = beta * current_S * current_I - gamma * current_I
dR = gamma * current_I
# Update values
next_S = current_S + dS * dt
next_I = current_I + dI * dt
next_R = current_R + dR * dt
next_t = current_t + dt
# Append to lists
S.append(next_S)
I.append(next_I)
R.append(next_R)
t.append(next_t)
n += 1
# Plot the results
plt.plot(t, S, label="Susceptible")
plt.plot(t, I, label="Infectious")
plt.plot(t, R, label="Recovered")
plt.xlabel("Time (days)")
plt.ylabel("Number of people")
plt.title("SIR Model for Akureyri disease")
plt.legend()
plt.grid(True)
plt.show()
References.
Bergmann, S. (2006, 10 10). Hvað er Akureyraveikin? Retrieved from Vísindavefurinn:
https://www.visindavefur.is/svar.php?id=6288#
Hethcote, H. W. (2000). The Mathematics of Infectious Diseases. SIAM Review, 4(42), 599-653.
doi:https://doi.org/10.1137/S0036144500371907.
Kermack, W. O. (1927). A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society A,
772(115), 700-721. doi:https://doi.org/10.1098/rspa.1927.0118.
Parish, J. G. (1978). Early outbreaks of “epidemic neuromyasthenia”. Postgraduate Medical Journal,
54, 711-717.
Pétursson, H. (29. mars 1996). Minningargrein um Sigurbjörgu Pétursdóttur. Morgunblaðið, 51.
Python Software Foundation. (2025, 08 02). Retrieved from Python 3 Documentation:
https://docs.python.org/
Sigurdsson, B. &. (1956). Clinical findings six years after outbreak of Akureyri disease. The Lancet,
270(6926), 766–767. doi:https://doi.org/10.1016/S0140-6736(56)91236-3.
Sigurdsson, B. S. (1950). A disease epidemic in Iceland simulating poliomyelitis. American Journal of Hygiene,
52(2), 222-238. doi:https://doi.org/10.1093/oxfordjournals.aje.a119421