Lotka-Volterra systems: dynamics and applications
Mathematical modelling can be used in a wide range of areas such as ecology, biology and finance. This was discussed in the presentation “Lotka-Volterra systems: dynamics and applications” by Helen Christodoulidi on 19/11/25.
Lotka-Volterra models can be used to demonstrate predator and prey populations over time. This is done through two non-linear first-order differential equations. When these equations are used, they do not form realistic results, as it is a toy model and only works for large data sets.
These equations are used to examine predator and prey, such as fox and rabbits, to show their population growth rates. In these equations, if the population of the prey is zero, then the population of the predator would decrease over time. Whereas, if the population of the predator is zero, the population of the prey would increase. If the two populations are at stable levels and graphed, it would form two wave formations, where the population of the predator would peak after the peak of the prey’s population.
This model can be adapted to represent epidemic models by making the predator the infected and the prey the healthy. This produces different models due to different parameters used, such as cure rates. This allows us to understand disease rates and predict future activity. [1]
In this type of model, there can be more than 2 variables. For example, it can be applied to 4 dimensions, which uses a community matrix. In some cases, 2 species survive, and 2 don’t, and in other cases, all 4 species survive. When these equations are plotted, they can be chaotic or organized. The graph can become organised if the cases are unbounded, and this can cause an example case where not all species survive. Additionally, the graph becomes chaotic if the cases are bounded. In this case, the graph becomes very complex, where all species survive.
Overall, the Lotka-Volterra models are solvable if they are 2D and have no elements of chaos. However, if the equations are in 4D, there are cases where it can be organised or chaotic. This model is useful for predicting changes in populations and can be adapted to predict changes in the markets.
[1] W. W. Mohammed, E. S. Aly, A. E. Matouk, and E. M. Elabbasy, “An analytical study of the dynamic behavior of Lotka-Volterra based models of COVID-19,” Results in Physics, vol. 26, no. 104432, Jul. 2021, doi: https://doi.org/10.1016/j.rinp.2021.104432
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Feedback based on the mark scheme provided is as follows:
Presentation: Title, name of speaker and date of seminar are provided. Grammar is generally good. Within the first line of the second paragraph, fox should be plural.
Content: Content mostly accurately covers what was discussed in the seminar, although some topics are a little underexplained. The phrasing of paragraph 4 sounds a bit misleading as you compare the model for epidemics with the predator-prey model. To improve, maybe compare with the x and y axes rather than with the previous model.
Context: Societal context is explained well.
Style: Writing style is good but fairly basic, and overall paragraphs could do with being a bit longer. It mostly would read well to a lay audience, however the term ‘community matrix’ is not explained.
External Source: References are correctly labelled, but could have done with more than one. No quoted opinions are present.
Overall it reads well but could have done with a bit more explanation and more references/quoted opinions to back up your points.
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The overall presentation is good, and you’ve included the date, title, and name of speaker. There are some cases in which you could use punctuation to make it a bit more readable; sentences with several commas get a bit confusing. Overall: Good
You’ve got the general message of the lecture, but some of the examples could use expanding on. For example, the example in the third paragraph is technically correct, it doesn’t really explain what the model does. Instead of saying the population of the predator/prey is 0, try saying if the population is decreasing. Also, when talking about modelling epidemics, the Lotka-Volterra model isn’t used, it’s a separate model called the SIR model. The lecture does focus on the Lotka-Volterra model, but overall is about dynamical systems, which I feel you’ve misunderstood. Overall: Good
You’ve done a good job of putting the use if mathematical modelling into context to explain why it is important. Overall: Excellent
You have an external source, which is good, but it doesn’t currently add any context that wasn’t mentioned in the lecture. The external source also isn’t a direct quote, which it needs to be according to the mark scheme. Overall: Poor
The writing style and technical level is mainly readable for a lay-person, but some terms are definitely not accessible to a layperson, like ‘non-linear first-order differential equations’ and ‘unbounded’. I don’t think it’s completely necessary to rigorously define these (you be there ages trying to), but it’d be useful to have maybe a short sentence about what this generally means, or replace them with easily to understand terminology. Overall: Good
Overall: This is a good recount of the lecture, but you need to be careful about solely talking about the Lotka-Volterra model when the lecture wasn’t just on that, it makes some of what you say technically wrong. It’s a strong draft and a great start! :)