Related papers: A four compartment epidemic model with retarded tr…
We study a coupled epidemic-mobility model in which, at each time, individuals move in a network of spatially-distributed regions (sub-populations) according to a Continuous Time Markov Chain (CTMC) and subsequently interact with the local…
Knowledge on the dynamics of standard epidemic models and their variants over complex networks has been well-established primarily in the stationary regime, with relatively little light shed on their transient behavior. In this paper, we…
In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…
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…
With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a…
We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the…
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…
Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
We consider an epidemiological model that includes waning and boosting of immunity. Assuming that repeated exposure to the pathogen fully restores immunity, we derive an SIRS-type model with discrete and distributed delays. First we prove…
Many epidemic models are naturally defined as individual-based models: where we track the state of each individual within a susceptible population. Inference for individual-based models is challenging due to the high-dimensional state-space…
Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type…
Parasite quiescence is the ability for the pathogen to be inactive, with respect to metabolism and infectiousness, for some amount of time and then become active (infectious) again. The population is thus composed of an inactive proportion,…
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…
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…
We introduce an epidemic model with varying infectivity and general exposed and infectious periods, where the infectivity of each individual is a random function of the elapsed time since infection, those function being i.i.d. for the…
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…