Mathematical Models in Population Biology and Epidemiology

By Fred Brauer, Carlos Castillo-Ch'avez. 2001

3,025 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b788bf8cc13109b410dfcf73de238fd4415f0002

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Citations in the corpus

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.”
Approximating the Stability Region for a Differential Equation with a Distributed Delay (2009, neutral): “wh en someone becomes infected with a disease they do not recover instantaneously but only after some period of time [8, 3].”
Compartmental Models in Epidemiology (2008, methodology): “Next, we will turn to some applications of SIR and SIS models, taken mainly from [3].”
Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks (2015, background): “sis is to consider the evolution of the total number of healthy and infected individuals rather than the state of each individual separately. This is commonly referred to as population dynamics [29], [30]. Furthermore, the recovery and infection rates are often assumed to be the same for all individ”
Complex dynamic behaviors of a discrete-time predator–prey system (2007, background): “We consider a Lotka–Volterra type predator–prey system [3,15] _ x 1⁄4 r0xð1 x kÞ b0xy; _ y 1⁄4 ð d0 þ cxÞy; ð1:3Þ where x(t) and y(t) denote prey and predator densities respectively, b0x is the predator functional response, which represents the number of prey individuals consumed per unit area per u”
Spatial-Temporal Dynamics in Nonlocal Epidemiological Models (2007, background): “Now consider the Diekmann-Thieme model (9) with Ω = R(n = 1, 2, 3).”
Multilayer networks (2013, background): “It is traditional to study spreading processes using compartmental models on completely mixed populations [11, 56].”
Nicholson's blowflies differential equations revisited: Main results and open problems (2010, background): “where m is a positive integer, together with the linear mortality term DðxÞ 1⁄4 dx; P > d > 0 or p=q > d > 0, respectively, satisfy all conditions ðA1Þ ðA3Þ and are widely used in fisheries [2].”
Efficient quantum algorithm for dissipative nonlinear differential equations (2020, methodology): “are decay rates and c ij 2R are pairwise nonlinear couplings. Equations of this type can be used to model interacting populations of predators and prey [48], the spread of infection during a pandemic [11], or the dynamics of chemical reactions [17,43]. Note that the r iu i term models exponential de”
Diffusive logistic equation with constant yield harvesting, I: Steady states (2002, result): “The equation (1.4) with (1.5) is a generalization of the wellknown ordinary dierential equation logistic model with constant yield harvesting (see [Cl], [ BC ]).”
A Fractional Order SEIR Model with Density Dependent Death Rate ABSTRACT | FULL TEXT (2011, background): “Introduction Mathematical modeling in epidemiology provides new aspects in understanding the spread of diseases, and it suggests control strategies [3].”