Thresholds and travelling waves for the geographical spread of infection

No abstract is available for this paper.

• Publication year

  1978

• Venue

  Journal of Mathematical Biology

• Publication date

  1978-07-27

• Fields of study

  Geography, Mathematics, Medicine

• Identifiers
  DOI 10.1007/BF02450783PMID 712253
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Asymptotic behavior of a model in population genetics

  1978cited by this paper
• Multidimensional nonlinear di u-sion arising in population genetics

  1978cited by this paper
• The epidemic in a closed population with all susceptibles equally vulnerable; some results for large susceptible populations and small initial infections

  1978cited by this paper
• On the bounded solutions of a nonlinear convolution equation

  1978cited by this paper
• The asymptotic behaviour of solutions of nonlinear integral equations

  1977cited by this paper
• A model for the spatial spread of an epidemic

  1977cited by this paper
• Limiting behaviour in an epidemic model

  1977influential reference
• Deterministic epidemic waves

  1976cited by this paper
• Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation

  1975cited by this paper
• Travelling fronts in nonlinear diffusion equations

  1975cited by this paper
• Mathematical Theories of Populations: Demographics, Genetics and Epidemics

  1975cited by this paper
• Possible velocities for a simple epidemic

  1972cited by this paper
• The rate of spatial propagation of simple epidemics

  1972cited by this paper
• Ordinary Differential Equations.

  1971cited by this paper
• An Introduction to Probability Theory and its Applications, Vol. II

  1967cited by this paper
• An Introduction to Probability Theory and Its Applications

  1967cited by this paper
• Studies on a convolution inequality

  1963cited by this paper
• An Introduction to Probability Theory and Its Applications

  1959cited by this paper
• Variabilità e concentrazione

  1957cited by this paper
• Introduction to the Theory of Fourier Integrals

  1938cited by this paper
• A contribution to the mathematical theory of epidemics

  1927cited by this paper

• Infinitely many saturated traveling waves for a degenerate Fisher-KPP equation not in divergence form

  2026cites this paper
• Traveling waves for SIR model on two-dimensional lattice

  2026cites this paper
• A one-parameter family of unbounded positive solutions for a class of nonlinear three-dimensional integral equations with an operator of the Hammerstein–Nemytsky type

  2025cites this paper
• Spatial propagation phenomena for diffusive SIS epidemic models

  2025cites this paper
• A Monotone Type Second-Order Numerical Method for Volterra–Fredholm Integro-Differential Equation

  2025cites this paper
• Constructive Solvability of a Class of Nonlinear Integral Equations of Urysohn Type

  2025cites this paper
• On the Constructive Solvability of One Class of Nonlinear Integral Equations of the Hammerstein Type on the Whole Line

  2025cites this paper
• The Shapes of Clines and Wavefronts

  2025cites this paper
• On the Solvability of a System of Multidimensional Integral Equations with Concave Nonlinearities

  2025cites this paper
• Mathematical epidemiology of infectious diseases: an ongoing challenge

  2025cites this paper
• Infinitely many saturated travelling waves for a degenerate Fisher-KPP equation not in divergence form

  2025cites this paper
• Dynamics of an epidemic model arising in a spatial segregation control strategy

  2025cites this paper
• Time periodic traveling wave solutions of a time-periodic reaction–diffusion SEIR epidemic model with periodic recruitment

  2025cites this paper
• Travelling wave dynamics in the nonlocal dispersal Fisher-KPP equation with distributed delay

  2025cites this paper
• Spreading dynamics of an SVIRS model.

  2025cites this paper
• On the Constructive Solvability of a Nonlinear Multidimensional Urysohn Equation in the Critical Case

  2025cites this paper
• Traveling Waves in a Reaction-Diffusion Addiction Epidemic Model with Distributed Delays

  2025cites this paper
• Existence and Uniqueness Theorems for One Class of Hammerstein-type Nonlinear Integral Equations

  2024cites this paper
• On the Solvability of an Infinite System of Algebraic Equations with Monotone and Concave Nonlinearity

  2024cites this paper
• Propagation phenomena of a vector-host disease model

  2024cites this paper
• Propagation dynamics in epidemic models with two latent classes

  2024cites this paper
• Numerical simulation of spatio-temporal spread of an infectious disease utilizing a collocation method based on local radial basis functions

  2024influential citation
• A Kermack–McKendrick type epidemic model with double threshold phenomenon (and a possible application to Covid-19)

  2024cites this paper
• An efficient computational method for nonlinear mixed Volterra–Fredholm integral equations

  2024cites this paper
• On the Qualitative Properties of a Solution to a System of Infinite Nonlinear Algebraic Equations

  2024cites this paper
• Constructive Study of Solvability for a Class of Nonlinear Integral Equations with a Symmetric Kernel

  2024cites this paper
• Spreading Speed in an Asymptotic Autonomous System with Application to a Diffusive Stage-Structured SLIRM Model

  2024cites this paper
• Traveling wave solutions of a susceptible-infectious model

  2024cites this paper
• Inequalities Applicable to Mixed Volterra-Fredholm Type Integral Equations

  2024cites this paper
• Periodic traveling waves for a diffusive influenza model with treatment and seasonality

  2024cites this paper
• Epidemic outbreaks in structured host populations

  2024cites this paper
• Traveling waves for a time-delayed nonlocal reaction-diffusion model of within-host viral infections

  2024cites this paper
• Final epidemic size of a two-community SIR model with asymmetric coupling

  2024cites this paper
• Long-time behavior of the heterogeneous SIRS epidemiological model

  2024cites this paper
• On the Constructive Solvability of one Class of the Hammerstein–Volterra type Nonlinear Multidimensional Integral Equations

  2024influential citation
• Projection and modified projection methods for nonlinear Hammerstein integral equations on the real line using Hermite polynomials

  2024cites this paper
• An accelerated iterative technique for solving mixed Fredholm-Volterra integral equations

  2024cites this paper
• A hybrid-based numerical method for a class of systems of mixed Volterra–Fredholm integral equations

  2024cites this paper
• Traveling Wavefronts to a Model of Precursor and Differentiated Cells: Impacting Parameter-Structure Transition from Monostable to Bistable, and from Monotone to Non-monotone

  2024cites this paper
• Functional Volterra Stieltjes integral equations and applications

  2024cites this paper
• Propagation threshold of a cooperative–competitive reaction–diffusion system

  2023cites this paper
• Spatially dense stochastic epidemic models with infection-age dependent infectivity

  2023influential citation
• Propagation dynamics in an SIRS model with general incidence functions.

  2023cites this paper
• On the Solvability of a System of Nonlinear Integral Equations with the Hammerstein–Stieltjes Operator on the Half-Line

  2023influential citation
• Gradient estimate for Fisher-KPP equation on Finsler metric measure spaces

  2023cites this paper
• Stationary States in Population Dynamics with Migration and Distributed Offspring

  2023cites this paper
• Spatial propagation phenomena for a diffusive epidemic model with vaccination

  2023cites this paper
• Epidemic Models with Varying Infectivity on a Refining Spatial Grid—I—The SI Model

  2023cites this paper
• On Solutions of a System of Nonlinear Integral Equations of Convolution Type on the Entire Real Line

  2023cites this paper
• Can infectious diseases eradicate host species? The effect of infection-age structure.

  2023cites this paper
• Propagation thresholds in a diffusive epidemic model with latency and vaccination

  2023cites this paper
• Solving Volterra integral equations via fourth-degree hat functions

  2023cites this paper
• Spreading Speed of a Cholera Epidemic Model in a Periodic Environment

  2023cites this paper
• Basic concepts for the Kermack and McKendrick model with static heterogeneity

  2023influential citation
• Uniqueness and stability analysis to a system of nonlocal partial differential equations related to an epidemic model

  2023cites this paper
• From localized to well mixed: How commuter interactions shape disease spread.

  2023cites this paper
• Uniqueness of the Solution of a Class of Integral Equations with Sum-Difference Kernel and with Convex Nonlinearity on the Positive Half-Line

  2023cites this paper
• AN ALGORITHM FOR APPROXIMATING SOLUTIONS OF SPLIT HAMMERSTEIN INTEGRAL EQUATIONS

  2023cites this paper
• Spatial Dynamics of Epidemic Models with Allee effect

  2023cites this paper
• Extended Runge-Kutta Scheme and Neural Network Approach for SEIR Epidemic Model with Convex Incidence Rate

  2023cites this paper
• On nonlinear convolution-type integral equations in the theory of $$p$$ -adic strings

  2023cites this paper
• Traveling wave solutions of a class of multi-species non-cooperative reaction–diffusion systems

  2023cites this paper
• Modelling coevolutionary dynamics in heterogeneous SI epidemiological systems across scales

  2023cites this paper
• Global stability and traveling wave solutions for some epidemiological models

  2023cites this paper
• Spatial Propagation for an Epidemic Model in a Patchy Environment

  2023cites this paper
• Boundedness of Traveling Waves in a Discrete Diffusion Model with Delay

  2023cites this paper
• Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis

  2022cites this paper
• Global stability and traveling wave solutions for a two-competing-prey and one-predator Lotka-Volterra model

  2022cites this paper
• A System of Integral Equations on the Entire Axis with Convex and Monotone Nonlinearity

  2022cites this paper
• Spreading speeds in two reaction-diffusion models for Polio disease

  2022cites this paper
• An efficient numerical method for a singularly perturbed Volterra-Fredholm integro-differential equation

  2022cites this paper
• Invariance-informed reduced-order sparse modeling of partial differential equations with DCA-ℓ1−2 algorithm

  2022cites this paper
• Linear and nonlinear minimal speed selection of traveling waves for a competitive system with nonlocal dispersal

  2022cites this paper
• Critical periodic traveling waves for a Kermack-McKendrick epidemic model with diffusion and seasonality

  2022cites this paper
• Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations

  2022cites this paper
• On One Class of Multidimensional Integral Equations of Convolution Type with Convex Nonlinearity

  2022cites this paper
• Propagation properties in a multi-species SIR reaction-diffusion system

  2022cites this paper
• The Hybrid Incidence Susceptible-Transmissible-Removed Model for Pandemics

  2022cites this paper
• Об одной системе интегральных уравнений на всей прямой с выпуклой и монотонной нелинейностью

  2022cites this paper
• SIR epidemic models with spatial spread in bounded domains

  2022cites this paper
• A PDE-ODE coupled spatio-temporal mathematical model for fire blight during bloom

  2022cites this paper
• On the numerical solutions for nonlinear Volterra-Fredholm integral equations

  2022cites this paper
• On the Constructive Solvability of a Two-Dimensional Nonlinear Integral Equation Arising in the Theory of $$p$$-Adic Strings

  2022cites this paper
• On Positive Bounded Solutions of One Class of Nonlinear Integral Equations with the Hammerstein–Nemytskii Operator

  2021cites this paper
• On Bounded Solutions of a Class of Nonlinear Integral Equations in the Plane and the Urysohn Equation in a Quadrant of the Plane

  2021cites this paper
• Traveling waves of nonlocal delayed disease models: critical wave speed and propagation speed

  2021cites this paper
• Про обмежені розв’язки одного класу нелінійних інтегральних рівнянь на площині та рівняння Урисона на чверті площини

  2021cites this paper
• Wave phenomena in a compartmental epidemic model with nonlocal dispersal and relapse

  2021cites this paper
• Speed determinacy of travelling waves for a three-component lattice Lotka–Volterra competition system

  2021cites this paper
• Exact description of SIR-Bass epidemics on 1D lattices

  2021cites this paper
• Non-monotone waves of a stage-structured SLIRM epidemic model with latent period

  2021cites this paper
• Propagation dynamics in a diffusive SIQR model for childhood diseases

  2021cites this paper
• Approximate solution of nonlinear Fredholm integral equations of the second kind using a class of Hermite interpolation polynomials

  2021cites this paper
• Solvability of a Certain System of Singular Integral Equations with Convex Nonlinearity on the Positive Half-Line

  2021cites this paper
• Nonlinear convolution type integral equations in complex spaces

  2021cites this paper
• Existence of traveling wave solutions for a delayed nonlocal dispersal SIR epidemic model with the critical wave speed.

  2021cites this paper
• On Solvability of a Class of Multidimensional Integral Equations in the Mathematical Theory of Geographic Distribution of an Epidemic

  2021cites this paper
• Numerical solutions of two-dimensional nonlinear integral equations via Laguerre Wavelet method with convergence analysis

  2021cites this paper
• Spreading dynamics of a Lotka-Volterra competition model in periodic habitats

  2021cites this paper
• Integral Equations on the Whole Line with Monotone Nonlinearity and Difference Kernel

  2021cites this paper