Related papers: Formulation a new SIR model with non-local mobilit…
This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We…
This paper examines a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and constant total population. The infection mechanism in the model is described by a nonlinear term of the form…
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…
The SIR model is a classical model characterizing the spreading of infectious diseases. This model describes the time-dependent quantity changes among Susceptible, Infectious, and Recovered groups. By introducing space-depend effects such…
Recently the A/H1N1-2009 virus pandemic appeared in Mexico and in other nations. We present a study of this pandemic in the Mexican case using the SIR model to describe epidemics. This model is one of the simplest models but it has been a…
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…
In the last decade, humanity has faced many different pandemics such as SARS, H1N1, and presently novel coronavirus (COVID-19). On one side, scientists are focusing on vaccinations, and on the other side, there is a need to propose models…
The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…
Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…
The surprisingly mercurial Covid-19 pandemic has highlighted the need to not only accelerate research on infectious disease, but to also study them using novel techniques and perspectives. A major contributor to the difficulty of containing…
Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the…
We propose an approach to model spatial heterogeneity in SIR-type models for the spread of epidemics via \emph{nonlocal aggregation terms}. More precisely, we first consider an SIR model with spatial movements driven by nonlocal aggregation…
In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and…
We revisit the classic Susceptible-Infected-Recovered (SIR) epidemic model and one of its nonlocal variations recently developed in \cite{Guan}. We introduce several new approaches to derive exact analytical solutions in the classical…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe…
Our study is based on an epidemiological compartmental model, the SIRS model. In the SIRS model, each individual is in one of the states susceptible (S), infected(I) or recovered (R), depending on its state of health. In compartment R, an…
In this work, the SIR epidemiological model is reformulated so to highlight the important {\em effective reproduction number}, as well as to account for the {\em generation time}, inverse of the {\em incidence rate}, and the {\em infectious…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…