Browsing by study line "Biomatematik"

Contacts between individuals play a central part in infectious disease modelling. Social or physical contacts are often determined through surveys. These types of contacts may not accurately represent the truly infectious contacts due to demographic differences in susceptibility and infectivity. In addition, surveyed data is prone to statistical biases and errors. For these reasons, a transmission model based on surveyed contact data may make predictions that are in conflict with real-life observations. The surveyed contact structure must be adjusted to improve the model and produce reliable predictions. The adjustment can be done in multiple different ways. We present five adjustment methods and study how the choice of method impacts a model’s predictions about vaccine effectiveness. The population is stratified into n groups. All five adjustment methods transform the surveyed contact matrix such that its normalised leading eigenvector (the model-predicted stable distribution of infections) matches the observed distribution of infections. The eigenvector method directly adjusts the leading eigenvector. It changes contacts antisymmetrically: if contacts from group i to group j increase, then contacts from j to i decrease, and vice versa. The susceptibility method adjusts the group-specific susceptibility of individuals. The changes in the contact matrix occur row-wise. Analogously, the infectivity method adjusts the group-specific infectivity; changes occur column-wise. The symmetric method adjusts susceptibility and infectivity in equal measure. It changes contacts symmetrically with respect to the main diagonal of the contact matrix. The parametrised weighting method uses a parameter 0 ≤ p ≤ 1 to weight the adjustment between susceptibility and infectivity. It is a generalisation of the susceptibility, infectivity and symmetric methods, which correspond to p = 0, p = 1 and p = 0.5, respectively. For demonstrative purposes, the adjustment methods were applied to a surveyed contact matrix and infection data from the COVID-19 epidemic in Finland. To measure the impact of the method on vaccination effectiveness predictions, the relative reduction of the basic reproduction number was computed for each method using Finnish COVID-19 vaccination data. We found that the eigenvector method has no impact on the relative reduction (compared to the unadjusted baseline case). As for the other methods, the predicted effectiveness of vaccination increased the more infectivity was weighted in the adjustment (that is, the larger the value of the parameter p). In conclusion, our study shows that the choice of adjustment method has an impact on model predictions, namely those about vaccination effectiveness. Thus, the choice should be considered when building infectious disease models. The susceptibility and symmetric methods seem the most natural choices in terms of contact structure. Choosing the ”optimal” method is a potential topic to explore in future research.

This work examines how neural networks can be used to qualitatively analyze systems of differential equations depicting population dynamics. We present a novel numerical method derived from physics informed learning, capable of extracting equilibria and bifurcations from population dynamics models. The potential of the framework is showcased three different example problems, a logistic model with outside inference, the Rosenzweig-MacArthur model and one model from a recent population dynamics paper. The key idea behind the method is having a neural network learn the dynamics of a free parameter ODE system, and then using the derivatives of the neural network to find equilibria and bifurcations. We, a bit clunkily, refer to these networks as physics informed neural networks with free parameters and variable initial conditions. In addition to these examples, we also survey how and where these neural networks could be further utilized in the context of population dynamics. To answer the how, we document our experiences choosing good hyperparameters for these networks, even venturing into previously unexplored territory. For the where, we suggest potentially useful neural network frameworks to answer questions from an external survey concerning contemporary open questions in population dynamics. The research of the work is preceded by a short dive on qualitative population dynamics, where we ponder what are the problems we want to solve and what are the tools we have available for that. Special attention is paid to parameter sensitivity analysis of ordinary differential equation systems through bifurcation theory. We also provide a beginner friendly introduction to deep learning, so that the research can be understood even by someone not previously familiar with the field. The work was written, and all included contents were selected, with the goal of establishing a basis for future research.

Pathogens are everywhere in nature, so organisms have developed various defense mechanisms in order to defend themselves against the pathogens. Two of the defense mechanisms are known as resistance and tolerance. Resistance describes the host's ability to avoid being infected by the pathogen, while tolerance describes the host's ability to reduce the fitness loss caused by the infection. We assume that investing into resistance reduces the transmission rate of the pathogens and investing into tolerance reduces the host's virulence. Developing the defense mechanisms is costly to the host. In this thesis, we assume that the resources invested into resistance and tolerance are taken away from the host's fecundity. The independent but simultaneous evolution of resistance and tolerance is modeled with an SIS model. The model is studied with the methods of adaptive dynamics. We concentrate on finding continuously stable strategies, which serve as the evolutionary end points for the population. We study the varying ecological parameters to determine which strategies are optimal for the host in different environments. We find that for low values of transmission rate, the hosts favor resistance over tolerance. When the transmission rate increases, resistance is traded for tolerance and the host benefits more from high tolerance. Low values of virulence result in tolerance being favored over resistance. Increasing virulence leads to a change in the defense mechanism as for high values of virulence investing into resistance is more beneficial to the host. The same holds for recovery rate, as tolerance is favored for low values of recovery rate and changed for resistance when the recovery rate increases. Patterns and associations between resistance and tolerance are also studied. Positive correlation between resistance and tolerance is found with low values of transmission rate, low and high values of virulence and high values of recovery rate. Resistance and tolerance correlate negatively with high values of transmission rate, intermediate values of virulence and low values of recovery rate.