Related papers: Various Logistic Curves in SIS and SIR Models
We discuss explicit solutions of the logistic model with variable parameters. Classical data on the sunflower seeds growth are revisited as a simple application of the logistic model with periodic coefficients. Some applications to related…
This paper considers the classical SIR epidemic model driven by a multidimensional L\'evy jump process. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. Our method differs from…
Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…
Compartmental models like the Susceptible-Infected-Recovered (SIR)\cite{Kermack1927} and its extensions such as the Susceptible-Exposed-Infected-Recovered (SEIRS)\cite{Ottar2020,Ignazio2021,Grimm2021,Paoluzzi2021} are commonly used to model…
Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the…
The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic SIR (Susceptible-Infective-Recovered) model on complex networks. It was found that in addition to the reduction of the effective…
In the absence of other tools, monitoring the effects of protective measures, including social distancing and forecasting the outcome of outbreaks is of immense interest. Real-time data is noisy and very often hampered by systematic errors…
The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are…
This document aims to estimate and describe the effects of the social distancing measures implemented in several countries with the expectancy of controlling the spread of COVID-19. The procedure relies on the classic…
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…
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…
Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…
Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…
The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…
We present three data driven model-types for COVID-19 with a minimal number of parameters to provide insights into the spread of the disease that may be used for developing policy responses. The first is exponential growth, widely studied…
Susceptible-Exposed-Infectious-Recovered (SEIR) models with inter-individual variation in susceptibility or exposure to infection were proposed early in the COVID-19 pandemic as a potential element of the mathematical/statistical toolset…
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…
Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary…
We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…
We consider the problem of identifying an infection source based only on an observed set of infected nodes in a network, assuming that the infection process follows a Susceptible-Infected-Susceptible (SIS) model. We derive an estimator…