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Register a new userGame theoretic modelling of infectious disease dynamics and intervention methods: a mini-review
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We review research papers which use game theory to model the decision making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. We show that the literature can be classified based on (i) type of population modelling (compartmental or network-based), (ii) frequency of the game (non-iterative or iterative), and (iii) type of strategy adoption (self-evaluation or imitation). We highlight that the choice of model depends on many factors such as the type of immunity the disease confers, the type of immunity the vaccine confers, and size of population and level of mixing therein. We show that while early studies used compartmental modelling with self-evaluation based strategy adoption, the recent trend is to use network-based modelling with imitation-based strategy adoption. Our review indicates that game theory continues to be an effective tool to model intervention (vaccination or social distancing) decision-making by individuals.
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We explore the application of probability generating functions (PGFs) to invasive processes, focusing on infectious disease introduced into large populations. Our goal is to acquaint the reader with applications of PGFs, moreso than to derive new results. PGFs help predict a number of properties about early outbreak behavior while the population is still effectively infinite, including the probability of an epidemic, the size distribution after some number of generations, and the cumulative size distribution of non-epidemic outbreaks. We show how PGFs can be used in both discrete-time and continuous-time settings, and discuss how to use these results to infer disease parameters from observed outbreaks. In the large population limit for susceptible-infected-recovered (SIR) epidemics PGFs lead to survival-function based models that are equivalent the the usual mass-action SIR models but with fewer ODEs. We use these to explore properties such as the final size of epidemics or even the dynamics once stochastic effects are negligible. We target this tutorial to biologists and public health researchers who want to learn how to apply PGFs to invasive diseases, but it could also be used in an introductory mathematics course on PGFs. We include many exercises to help demonstrate concepts and to give practice applying the results. We summarize our main results in a few tables. Additionally we provide a small python package which performs many of the relevant calculations.
Background: Analysing tumour architecture for metastatic potential usually focuses on phenotypic differences due to cellular morphology or specific genetic mutations, but often ignore the cells position within the heterogeneous substructure. Similar disregard for local neighborhood structure is common in mathematical models. Methods: We view the dynamics of disease progression as an evolutionary game between cellular phenotypes. A typical assumption in this modeling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard local heterogeneities. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go vs. grow game. Results: We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary -- such as a blood-vessel, organ capsule, or basement membrane -- we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (EMT positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Interpretation: Pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. We expect our approach to extend to other evolutionary game models where interaction neighborhoods change at fixed system boundaries.
Major advances in public health have resulted from disease prevention. However, prevention of a new infectious disease by vaccination or pharmaceuticals is made difficult by the slow process of vaccine and drug development. We propose an additional intervention that allows rapid control of emerging infectious diseases, and can also be used to eradicate diseases that rely almost exclusively on human-to-human transmission. The intervention is based on (1) testing every individual for the disease, (2) repeatedly, and (3) isolation of infected individuals. We show here that at a sufficient rate of testing, the reproduction number is reduced below 1.0 and the epidemic will rapidly collapse. The approach does not rely on strong or unrealistic assumptions about test accuracy, isolation compliance, population structure or epidemiological parameters, and its success can be monitored in real time by following the test positivity rate. In addition to the compliance rate and false negatives, the required rate of testing depends on the design of the testing regime, with concurrent testing outperforming random sampling. Provided that results are obtained rapidly, the test frequency required to suppress an epidemic is monotonic and near-linear with respect to R0, the infectious period, and the fraction of susceptible individuals. The testing regime is effective against both early phase and established epidemics, and additive to other interventions (e.g. contact tracing and social distancing). It is also robust to failure: any rate of testing reduces the number of infections, improving both public health and economic conditions. These conclusions are based on rigorous analysis and simulations of appropriate epidemiological models. A mass-produced, disposable test that could be used at home would be ideal, due to the optimal performance of concurrent tests that return immediate results.
School environments are thought to play an important role in the community spread of airborne infections (e.g., influenza) because of the high mixing rates of school children. The closure of schools has therefore been proposed as efficient mitigation strategy, with however high social and economic costs: alternative, less disruptive interventions are highly desirable. The recent availability of high-resolution contact networks in school environments provides an opportunity to design micro-interventions and compare the outcomes of alternative mitigation measures. We consider mitigation measures that involve the targeted closure of school classes or grades based on readily available information such as the number of symptomatic infectious children in a class. We focus on the case of a primary school for which we have high-resolution data on the close-range interactions of children and teachers. We simulate the spread of an influenza-like illness in this population by using an SEIR model with asymptomatics and compare the outcomes of different mitigation strategies. We find that targeted class closure affords strong mitigation effects: closing a class for a fixed period of time -equal to the sum of the average infectious and latent durations- whenever two infectious individuals are detected in that class decreases the attack rate by almost 70% and strongly decreases the probability of a severe outbreak. The closure of all classes of the same grade mitigates the spread almost as much as closing the whole school. Targeted class closure strategies based on readily available information on symptomatic subjects and on limited information on mixing patterns, such as the grade structure of the school, can be almost as effective as whole-school closure, at a much lower cost. This may inform public health policies for the management and mitigation of influenza-like outbreaks in the community.
Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious diseases. In other words, mathematical model simulation can be used to analyse the dynamics of infectious diseases, aiming to understand the effects and how to control the spread. In general, these models are based on compartments, where each compartment contains individuals with the same characteristics, such as susceptible, exposed, infected, and recovered. In this paper, we cast further light on some classical epidemic models, reporting possible outcomes from numerical simulation. Furthermore, we provide routines in a repository for simulations.
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