6,700
Views
71
CrossRef citations to date
0
Altmetric
Original Articles

On the formulation of epidemic models (an appraisal of Kermack and McKendrick)

, , , &
Pages 103-117 | Received 15 May 2012, Accepted 24 Jul 2012, Published online: 17 Aug 2012

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (1)

O. Diekmann & K. Korvasová. (2013) A didactical note on the advantage of using two parameters in Hopf bifurcation studies. Journal of Biological Dynamics 7:sup1, pages 21-30.
Read now

Articles from other publishers (70)

Maximilian M. Nguyen, Ari S. Freedman, Sinan A. Ozbay & Simon A. Levin. (2023) Fundamental bound on epidemic overshoot in the SIR model. Journal of The Royal Society Interface 20:209.
Crossref
Alessia Andò & Dimitri Breda. (2023) Piecewise orthogonal collocation for computing periodic solutions of renewal equations. Advances in Computational Mathematics 49:6.
Crossref
Ibrahim Bouzalmat, Mourad El Idrissi, Adel Settati & Aadil Lahrouz. (2023) Stochastic SIRS epidemic model with perturbation on immunity decay rate. Journal of Applied Mathematics and Computing.
Crossref
Mohamed M. A. Metwali & Kinga Cichoń. (2023) Solvability of the product of n-integral equations in Orlicz spaces. Rendiconti del Circolo Matematico di Palermo Series 2.
Crossref
Biplab Maity, Swarnendu Banerjee, Abhishek Senapati & Joydev Chattopadhyay. (2023) Quantifying optimal resource allocation strategies for controlling epidemics. Journal of The Royal Society Interface 20:202.
Crossref
Florin Avram, Rim Adenane, Lasko Basnarkov, Gianluca Bianchin, Dan Goreac & Andrei Halanay. (2023) An Age of Infection Kernel, an R Formula, and Further Results for Arino–Brauer A, B Matrix Epidemic Models with Varying Populations, Waning Immunity, and Disease and Vaccination Fatalities. Mathematics 11:6, pages 1307.
Crossref
Odo Diekmann & Hisashi Inaba. (2023) A systematic procedure for incorporating separable static heterogeneity into compartmental epidemic models. Journal of Mathematical Biology 86:2.
Crossref
Nicola Guglielmi, Elisa Iacomini & Alex Viguerie. (2023) Identification of time delays in COVID-19 data. Epidemiologic Methods 12:1.
Crossref
Eleonora Messina, Mario Pezzella & Antonia Vecchio. (2023) Nonlocal finite difference discretization of a class of renewal equation models for epidemics. AIMS Mathematics 20:7, pages 11656-11675.
Crossref
Ottar N. BjørnstadOttar Bjørnstad. 2023. Epidemics. Epidemics 11 32 .
Esteban A. Hernandez-Vargas, Alejandro H. Gonzalez, Carolyn L. Beck, Xiaoqi Bi, Francesca Cala Campana & Giulia Giordano. (2022) Modelling and Control of Epidemics Across Scales. Modelling and Control of Epidemics Across Scales.
Ruili Fan & Stefan A.H. Geritz. (2022) Modelling and optimising healthcare interventions in a model with explicit within- and between-host dynamics. Journal of Theoretical Biology 554, pages 111276.
Crossref
Natali Hritonenko & Yuri Yatsenko. (2022) Analysis of optimal lockdown in integral economic–epidemic model. Economic Theory.
Crossref
Natali Hritonenko, Caroline Satsky & Yuri Yatsenko. (2022) INTEGRAL MODEL OF COVID-19 SPREAD AND MITIGATION IN UK: IDENTIFICATION OF TRANSMISSION RATE. Mathematical Modelling and Analysis 27:4, pages 573-589.
Crossref
Mohamed M.A. Metwali. (2022) Solvability in weighted L1-spaces for the m-product of integral equations and model of the dynamics of the capillary rise. Journal of Mathematical Analysis and Applications 515:2, pages 126461.
Crossref
Malú Grave, Alex Viguerie, Gabriel F. Barros, Alessandro Reali, Roberto F.S. Andrade & Alvaro L.G.A. Coutinho. (2022) Modeling nonlocal behavior in epidemics via a reaction–diffusion system incorporating population movement along a network. Computer Methods in Applied Mechanics and Engineering 401, pages 115541.
Crossref
Natali Hritonenko, Olga Yatsenko & Yuri Yatsenko. (2021) Model with transmission delays for COVID‐19 control: Theory and empirical assessment. Journal of Public Economic Theory 24:5, pages 1218-1244.
Crossref
Simone Raponi, Zeinab Khalifa, Gabriele Oligeri & Roberto Di Pietro. (2022) Fake News Propagation: A Review of Epidemic Models, Datasets, and Insights. ACM Transactions on the Web 16:3, pages 1-34.
Crossref
Sang Woo Park, Benjamin M. Bolker, Sebastian Funk, C. Jessica E. Metcalf, Joshua S. Weitz, Bryan T. Grenfell & Jonathan Dushoff. (2022) The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants. Journal of The Royal Society Interface 19:191.
Crossref
Romain Ducasse. (2022) Threshold phenomenon and traveling waves for heterogeneous integral equations and epidemic models. Nonlinear Analysis 218, pages 112788.
Crossref
Ateq Alsaadi, Mieczysław Cichoń & Mohamed M. A. Metwali. (2022) Integrable Solutions for Gripenberg-Type Equations with m-Product of Fractional Operators and Applications to Initial Value Problems. Mathematics 10:7, pages 1172.
Crossref
Ferdinand Pfab, Roger M. Nisbet & Cheryl J. Briggs. (2022) A time-since-infection model for populations with two pathogens. Theoretical Population Biology 144, pages 1-12.
Crossref
Matthias Kreck & Erhard Scholz. (2022) Back to the Roots: A Discrete Kermack–McKendrick Model Adapted to Covid-19. Bulletin of Mathematical Biology 84:4.
Crossref
Reynaldo Ortiz, Alexey Egorov & Sabine Mondié. (2021) Necessary and sufficient stability conditions for integral delay systems. International Journal of Robust and Nonlinear Control 32:6, pages 3152-3174.
Crossref
Alex Viguerie, Gabriel F. Barros, Malú Grave, Alessandro Reali & Alvaro L.G.A. Coutinho. (2022) Coupled and uncoupled dynamic mode decomposition in multi-compartmental systems with applications to epidemiological and additive manufacturing problems. Computer Methods in Applied Mechanics and Engineering 391, pages 114600.
Crossref
Burcu Gürbüz, Herman Mawengkang, Ismail Husein & Gerhard-Wilhelm Weber. (2021) Rumour propagation: an operational research approach by computational and information theory. Central European Journal of Operations Research 30:1, pages 345-365.
Crossref
Andjelka B. Kovačević. (2022) On possible life-dispersal patterns beyond the Earth. International Journal of Astrobiology, pages 1-18.
Crossref
Eleonora Messina, Mario Pezzella & Antonia Vecchio. (2022) Positive Numerical Approximation of Integro-Differential Epidemic Model. Axioms 11:2, pages 69.
Crossref
Eleonora Messina, Mario Pezzella & Antonia Vecchio. (2022) A non-standard numerical scheme for an age-of-infection epidemic model. Journal of Computational Dynamics 9:2, pages 239.
Crossref
François G. Schmitt. (2021) An algorithm for the direct estimation of the parameters of the SIR epidemic model from the I(t) dynamics. The European Physical Journal Plus 137:1.
Crossref
Fabio Vanni, David Lambert, Luigi Palatella & Paolo Grigolini. (2021) On the use of aggregated human mobility data to estimate the reproduction number. Scientific Reports 11:1.
Crossref
Alessia Andò. (2021) Convergence of collocation methods for solving periodic boundary value problems for renewal equations defined through finite‐dimensional boundary conditions. Computational and Mathematical Methods 3:6.
Crossref
Odo Diekmann, Hans G. Othmer, Robert Planqué & Martin C. J. Bootsma. (2021) The discrete-time Kermack–McKendrick model: A versatile and computationally attractive framework for modeling epidemics. Proceedings of the National Academy of Sciences 118:39.
Crossref
Enrico Schiassi, Mario De Florio, Andrea D’Ambrosio, Daniele Mortari & Roberto Furfaro. (2021) Physics-Informed Neural Networks and Functional Interpolation for Data-Driven Parameters Discovery of Epidemiological Compartmental Models. Mathematics 9:17, pages 2069.
Crossref
Luigi Palatella, Fabio Vanni & David Lambert. (2021) A phenomenological estimate of the true scale of CoViD-19 from primary data. Chaos, Solitons & Fractals 146, pages 110854.
Crossref
Francesca Scarabel, Lorenzo Pellis, Nicholas H. Ogden & Jianhong Wu. (2021) A renewal equation model to assess roles and limitations of contact tracing for disease outbreak control. Royal Society Open Science 8:4.
Crossref
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Andrea Pugliese & Mattia Sensi. (2021) A geometric analysis of the SIR, SIRS and SIRWS epidemiological models. Nonlinear Analysis: Real World Applications 58, pages 103220.
Crossref
Teodoro Alamo, Daniel G. Reina, Pablo Millán Gata, Victor M. Preciado & Giulia Giordano. (2021) Data-driven methods for present and future pandemics: Monitoring, modelling and managing. Annual Reviews in Control 52, pages 448-464.
Crossref
Aubain Nzokem & Neal Madras. 2021. Recent Developments in Mathematical, Statistical and Computational Sciences. Recent Developments in Mathematical, Statistical and Computational Sciences 591 599 .
Giulia Giordano & Fabrizio Dabbene. 2021. Encyclopedia of Systems and Control. Encyclopedia of Systems and Control 1292 1301 .
Dimitri Breda & Davide Liessi. (2020) Approximation of eigenvalues of evolution operators for linear coupled renewal and retarded functional differential equations. Ricerche di Matematica 69:2, pages 457-481.
Crossref
Mahnaz Alavinejad & Jianhong Wu. (2019) Coupled Systems of Renewal Equations for Forces of Infection through a Contact Network. Canadian Mathematical Bulletin 63:3, pages 624-632.
Crossref
Patricio Olivares, Werner Creixell & Naoya Fujiwara. (2020) Dynamical impacts of the coupling in a model of interactive infectious diseases. Chaos: An Interdisciplinary Journal of Nonlinear Science 30:9.
Crossref
Aubain Nzokem & Neal Madras. (2020) Epidemic Dynamics and Adaptive Vaccination Strategy: Renewal Equation Approach. Bulletin of Mathematical Biology 82:9.
Crossref
Dimitri Breda & Davide Liessi. (2020) Floquet Theory and Stability of Periodic Solutions of Renewal Equations. Journal of Dynamics and Differential Equations.
Crossref
Alessia Andò & Dimitri Breda. 2020. Current Trends in Dynamical Systems in Biology and Natural Sciences. Current Trends in Dynamical Systems in Biology and Natural Sciences 43 62 .
Giulia Giordano & Fabrizio Dabbene. 2020. Encyclopedia of Systems and Control. Encyclopedia of Systems and Control 1 10 .
Jorge A. Alfaro-Murillo, Zhilan Feng & John W. Glasser. (2019) Analysis of an epidemiological model structured by time-since-last-infection. Journal of Differential Equations 267:10, pages 5631-5661.
Crossref
Aniruddha Deka & Samit Bhattacharyya. (2019) Game dynamic model of optimal budget allocation under individual vaccination choice. Journal of Theoretical Biology 470, pages 108-118.
Crossref
Michael T. Meehan, Daniel G. Cocks, Johannes Müller & Emma S. McBryde. (2019) Global stability properties of a class of renewal epidemic models. Journal of Mathematical Biology 78:6, pages 1713-1725.
Crossref
Fred Brauer, Carlos Castillo-Chavez & Zhilan FengFred Brauer, Carlos Castillo-Chavez & Zhilan Feng. 2019. Mathematical Models in Epidemiology. Mathematical Models in Epidemiology 3 19 .
Andrea Pugliese & Fabio Milner. (2018) A structured population model with diffusion in structure space. Journal of Mathematical Biology 77:6-7, pages 2079-2102.
Crossref
Mats Gyllenberg, Francesca Scarabel & Rossana Vermiglio. (2018) Equations with infinite delay: Numerical bifurcation analysis via pseudospectral discretization. Applied Mathematics and Computation 333, pages 490-505.
Crossref
Gabriela Marinoschi. (2018) A model of an epidemic mapping. Ricerche di Matematica 67:1, pages 271-284.
Crossref
David Champredon, Jonathan Dushoff & David J. D. Earn. (2018) Equivalence of the Erlang-Distributed SEIR Epidemic Model and the Renewal Equation. SIAM Journal on Applied Mathematics 78:6, pages 3258-3278.
Crossref
Dimitri Breda & Davide Liessi. (2018) Approximation of Eigenvalues of Evolution Operators for Linear Renewal Equations. SIAM Journal on Numerical Analysis 56:3, pages 1456-1481.
Crossref
Ottar N. BjørnstadOttar N. Bjørnstad. 2018. Epidemics. Epidemics 9 30 .
Fred Brauer. (2017) Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling 2:2, pages 113-127.
Crossref
Thomas W. Carr. (2017) Equivalent probability density moments determine equivalent epidemics in an SIRS model with temporary immunity. Theoretical Population Biology 113, pages 47-55.
Crossref
Hisashi InabaHisashi Inaba. 2017. Age-Structured Population Dynamics in Demography and Epidemiology. Age-Structured Population Dynamics in Demography and Epidemiology 379 442 .
Stelian Ion & Gabriela Marinoschi. (2016) A self-organizing criticality mathematical model for contamination and epidemic spreading. Discrete and Continuous Dynamical Systems - Series B 22:2, pages 383-405.
Crossref
Ottar N. Bjørnstad, William A. Nelson & Patrick C. Tobin. (2016) Developmental synchrony in multivoltine insects: generation separation versus smearing. Population Ecology 58:4, pages 479-491.
Crossref
Thomas W. Carr. (2016) An SIRS epidemic model with a rapidly decreasing probability for immunity. IMA Journal of Applied Mathematics 81:2, pages 281-307.
Crossref
Cameron Nowzari, Victor M. Preciado & George J. Pappas. (2016) Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks. IEEE Control Systems 36:1, pages 26-46.
Crossref
M. V. Barbarossa & G. R?st. (2015) Immuno-epidemiology of a population structured by immune status: a mathematical study of waning immunity and immune system boosting. Journal of Mathematical Biology 71:6-7, pages 1737-1770.
Crossref
Damian Clancy. (2015) Generality of endemic prevalence formulae. Mathematical Biosciences 269, pages 30-36.
Crossref
Lorenzo Pellis, Simon E.F. Spencer & Thomas House. (2015) Real-time growth rate for general stochastic SIR epidemics on unclustered networks. Mathematical Biosciences 265, pages 65-81.
Crossref
Mick Roberts, Viggo Andreasen, Alun Lloyd & Lorenzo Pellis. (2015) Nine challenges for deterministic epidemic models. Epidemics 10, pages 49-53.
Crossref
Alberto Gandolfi, Andrea Pugliese & Carmela Sinisgalli. (2014) Epidemic dynamics and host immune response: a nested approach. Journal of Mathematical Biology 70:3, pages 399-435.
Crossref
Yukihiko Nakata, Yoichi Enatsu, Hisashi Inaba, Toshikazu Kuniya, Yoshiaki Muroya & Yasuhiro Takeuchi. (2014) Stability of epidemic models with waning immunity. SUT Journal of Mathematics 50:2.
Crossref