Related papers: Navigating Epidemic Mathematics: Exploring Tools f…
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
As global living standards improve and medical technology advances, many infectious diseases have been effectively controlled. However, certain diseases, such as the recent COVID-19 pandemic, continue to pose significant threats to public…
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…
Malware attacks in today's vast digital ecosystem pose a serious threat. Understanding malware propagation dynamics and designing effective control strategies are therefore essential. In this work, we propose a generic SEIRV model…
In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR)…
In this work, we review the figures used to characterize an epidemic outbreak most. Particular attention is drawn to epidemic spreading at time-varying transition rates. A time-varying SIR-like model is used to describe the epidemic…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete…
In this work we analyze mathematically the consequences and effectiveness of strategies to control an epidemic in the framework of classical SEIR models with multiple parallel infectious stages. We define the mathematical concept of a…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
The study of epidemic models plays an important role in mathematical epidemiology. There are many researches on epidemic models using ordinary differential equations, partial differential equations or stochastic differential equations. In…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
In this project, identifiability, observability and uncertainty properties of the deterministic and Chain Binomial stochastic SIR, SEIR and SEIAR epidemiological models are studied. Techniques for modeling overdispersion are investigated…
During an infectious disease outbreak, biases in the data and complexities of the underlying dynamics pose significant challenges in mathematically modelling the outbreak and designing policy. Motivated by the ongoing response to COVID-19,…
Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…
We perform a bifurcation analysis on an SIR model involving two pathogens that influences each other. Partial cross-immunity is assumed and coinfection is thought to be less transmittable then each of the diseases alone. The susceptible…
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 consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…
The existence and local stability of some non-negative equilibrium points of a class of SIRS infectious disease models with non-linear infection and treatment rates are investigated under the condition that the total population is a…