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An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discretization, since the discretization is based on the…

Exactly Solvable and Integrable Systems · Physics 2023-03-31 Atsushi Nobe

We set up the Dirac equation in a Friedmann-Robertson-Walker geometry and separate the spatial and time variables. In the case of a closed universe, the spatial dependence is solved explicitly, giving rise to a discrete set of solutions. We…

Mathematical Physics · Physics 2013-02-07 Felix Finster , Moritz Reintjes

Starting with the Dirac equation in the extreme Kerr metric we derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the class of smooth compactly supported functions.

General Relativity and Quantum Cosmology · Physics 2008-11-26 D. Batic , H. Schmid

By means of numerical simulations and epidemic analysis, the transition point of the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a square lattice is found to be c_0=0.1765005(10), where c is the probability a…

Disordered Systems and Neural Networks · Physics 2010-11-18 Tânia Tomé , Robert M. Ziff

The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…

Populations and Evolution · Quantitative Biology 2020-11-17 Christian Gourieroux , Yang Lu

We derive solvability conditions and closed-form solution for the Weber type integral equation, related to the familiar Weber-Orr integral transforms and the old Weber-Titchmarsh problem (posed in Proc. Lond. Math. Soc. 22 (2) (1924),…

Classical Analysis and ODEs · Mathematics 2017-01-17 Semyon Yakubovich

In this paper, we introduce a general framework for co-infection as cooperative SIR dynamics. We first solve analytically CGCG model [1] and then the generalized model in symmetric scenarios. We calculate transition points, order parameter,…

Populations and Evolution · Quantitative Biology 2019-07-24 Fatemeh Zarei , Saman Moghimi-Araghi , Fakhteh Ghanbarnejad

I estimate the Susceptible-Infected-Recovered (SIR) epidemic model for Coronavirus Disease 2019 (COVID-19). The transmission rate is heterogeneous across countries and far exceeds the recovery rate, which enables a fast spread. In the…

Populations and Evolution · Quantitative Biology 2020-03-27 Alexis Akira Toda

Motivated by the classical Susceptible-Infected-Recovered (SIR) epidemic models proposed by Kermack and Mckendrick, we consider a class of stochastic compartmental dynamical systems with a notion of partial ordering among the compartments.…

Populations and Evolution · Quantitative Biology 2019-01-03 Wasiur R. KhudaBukhsh , Boseung Choi , Eben Kenah , Grzegorz A. Rempala

We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…

Probability · Mathematics 2019-03-28 Pierre Montagnon

We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where…

Statistical Mechanics · Physics 2009-11-10 Yamir Moreno , Javier B. Gomez , Amalio F. Pacheco

In previous work by this author, the screening paradox - the loss of predictive power of screening tests over time $t$ - was mathematically formalized using Bayesian theory. Where $J$ is Youden's statistic, $b$ is the specificity of the…

Methodology · Statistics 2021-04-19 Jacques Balayla

In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for…

Dynamical Systems · Mathematics 2023-07-20 Moritz Schäfer , Karol Niedzielewski , Thomas Götz , Tyll Krüger

An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…

Optimization and Control · Mathematics 2013-08-19 Wolf-Jürgen Beyn , Janosch Rieger

We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a…

Physics and Society · Physics 2012-06-28 Andrew Lucas

We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity…

Populations and Evolution · Quantitative Biology 2020-04-09 C. P. Vyasarayani , Anindya Chatterjee

In this work, some new exact and approximate analytical solutions are obtained for the SIR epidemic model, which is formulated in terms of dimensionless variables and parameters. The susceptibles population (S) is in this way explicitly…

Populations and Evolution · Quantitative Biology 2020-09-04 Mario Berberan-Santos

In this article we investigate and solve exactly the modified Dirac oscillator in curved spacetime with spin and pseudospin symmetries through an algebraic approach. By focusing on the radial part of this problem, we use the Schr\"odinger…

We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…

Analysis of PDEs · Mathematics 2025-12-16 Giorgio Martalò , Giuseppe Toscani , Mattia Zanella

When homogenizing elliptic partial differential equations, the so-called corrector problem is pivotal to compute the macroscale effective coefficients from the microscale information. To solve this corrector problem in the periodic setting,…

Numerical Analysis · Mathematics 2014-11-04 Sebastien Brisard , Frederic Legoll