Mathematics in Population Biology

By Horst R. Thieme. 2003

1,118 citations recorded by the source corpus.

The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies. Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a "toolbox" provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided. The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/4884bbc399137c7e9d80cba1f394b33430346923

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Citations in the corpus

Spatial-Temporal Dynamics in Nonlocal Epidemiological Models (2007, background): “…model and the threshold result derived from it have played a pivotal role in subsequent developments in the study of the transmission dynamics of infective diseases (Anderson and May 1991; Brauer and Castillo-Chavez 2000; Diekmann and Heesterbeek 2000; Hethcote 2000; Thieme 2003).”
A Simplified Dynamical System for Tropical Cyclone Intensity Prediction (2009, methodology): “The analytic solution of (3) with constant coefficients is described by Thieme (2003) in the context of population modeling.”
Local stability implies global stability in some one-dimensional discrete single-species models (2006, methodology): “For the general case, it is claimed in [10] that there is a gap between the local stability condition x̄(1− q) ≤ 2, where x̄ = ln(γ/(1− q)) is the positive equilibrium, and the known global stability conditions.”
Dynamical Systems And Population Persistence (2016, background): “See Freedman and Moson [72] for flows on locally compact metric spaces, Freedman, Ruan, and Tang [73] for flows, and Thieme [215] for semiflows on general metric spaces.”
Global-stability problem for coupled systems of differential equations on networks (2010, background): “For detailed discussions of the model and interpretations of parameters, we refer the reader to [15,34].”
Permanence of a delayed SIR epidemic model with density dependent birth rate (2007, background): “Epidemic models with or without time delay are studied by many authors (see, for example, for the model with time delay [1,2,11–13,15], for one without time delay [7,9,10,14]).”
Role of Fear in a Predator–Prey Model with Beddington–DeAngelis Functional Response (2019, neutral): “To prove this, we follow the theorem given in [41].”
Traveling wavefronts for time-delayed reaction-diffusion equation: (II) Nonlocal nonlinearity (2009, background): “Proof of nonlinear stability As shown in [16] (see also [9,15,27]), one can similarly prove the following boundedness and the comparison principle.”
Compartmental Models in Epidemiology (2008, neutral): “11–14, and [2,4–6,9, 17,29,35].”
MATHEMATICAL ANALYSIS OF AN AGE-STRUCTURED SIR EPIDEMIC MODEL WITH VERTICAL TRANSMISSION (2005, background): “1Strictly speaking, here r(T (0)) should not be called as the basic reproduction ratio but could be called as the net replacement ratio (see Thieme [48], p.”
The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models (2005, methodology): “Dynamical population models are used to predict average behavior, generate hypotheses or explore mechanisms across many fields of science including ecology [1–3], epidemiology [4–7] and immunology [8], to name but a few.”
A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients (2010, background): “1 Introduction Models describing the time evolution of physiologically structured populations have been extensively studied for many years [20,27,30].”