相关论文: Some approximate solutions to the spread of influe…

We develop simple models for the global spread of infectious diseases, emphasizing human mobility via air travel and the variation of public health infrastructure from region to region. We derive formulas relating the total and peak number…

Viral kinetics have been extensively studied in the past through the use of spatially homogeneous ordinary differential equations describing the time evolution of the diseased state. However, spatial characteristics such as localized…

The evolutionary dynamics of human Influenza A virus presents a challenging theoretical problem. An extremely high mutation rate allows the virus to escape, at each epidemic season, the host immune protection elicited by previous…

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…

The aim of this paper is to present an, admittedly somewhat subjective, bird's eye view of the mathematical theory concerning the spread of an infectious disease in a susceptible host population with static structure, culminating in a…

A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…

Within the human respiratory tract (HRT), viruses diffuse through the periciliary fluid (PCF) bathing the epithelium, and travel upwards via advection towards the nose and mouth, as the mucus escalator entrains the PCF. While many…

A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity are…

We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…

A mathematical model for estimating the risk of airborne transmission of a respiratory infection such as COVID-19, is presented. The model employs basic concepts from fluid dynamics and incorporates the known scope of factors involved in…

The field of epidemiology has presented fascinating and relevant questions for mathematicians, primarily concerning the spread of viruses in a community. The importance of this research has greatly increased over time as its applications…

Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized…

The appearance of the coronavirus (COVID-19) in late 2019 has dominated the news in the last few months as it developed into a pandemic. In many mathematics and physics classrooms, instructors are using the time series of the number of…

Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics,…

An individual-based model of the infectious disease spread among the urban population is considered. A system of stochastic equations, which describes changes in quantities of four population groups, susceptible, exposed, infected…

We introduce and discuss a minimal individual-based model for influenza dynamics. The model takes into account the effects of specific immunization against viral strains, but also infectivity randomness and the presence of a short-lived…

Modelling the transmission dynamics of an infectious disease is a complex task. Not only it is difficult to accurately model the inherent non-stationarity and heterogeneity of transmission, but it is nearly impossible to describe,…

This paper investigates the dynamics of infectious diseases with a non-exponentially distributed infectious period. This is achieved by considering a multi-stage infection model on networks. Using pairwise approximation with a standard…

Disease outbreaks, such as those of Severe Acute Respiratory Syndrome in 2003 and the 2009 pandemic A(H1N1) influenza, have highlighted the potential for airborne transmission in indoor environments. Respirable pathogen-carrying droplets…