Related papers: Threshold dynamics in a within host infection mode…
Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…
A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have been proposed and studied. The basic reproductive number $R_0$ is defined. The dynamical behaviors of the model are analyzed with the help of persistence,…
In this paper we put forward a viral propagation model with nonlinear infection rate and free boundaries and investigate the dynamical properties. This model is composed of two ordinary differential equations and one partial differential…
Physiological stress fundamentally alters disease susceptibility in aquatic environments. In this paper, we develop a stress-structured epidemiological model where host vulnerability is dynamically driven by water quality. Analytically, we…
In this paper, a mathematical analysis of the global dynamics of a partial differential equation viral infection cellular model is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both…
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally…
In this paper we propose a malaria within-host model with k classes of age for the parasitized red blood cells and n strains for the parasite. We provide a global analysis for this model. A competitive exclusion principle holds. If R0, the…
Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($\sigma_{inh}$) and external infectivity ($\iota_{ext}$), in a given population.…
The basic reproduction number ($R_0$) is an epidemiological metric that represents the average number of new infections caused by a single infectious individual in a completely susceptible population. The methodology for calculating this…
The dynamics of epidemic spreading is often reduced to the single control parameter $R_0$, whose value, above or below unity, determines the state of the contagion. If, however, the pathogen evolves as it spreads, $R_0$ may change over…
As the outbreak of COVID-19 enters its third year, we have now enough data to analyse the behavior of the pandemic with mathematical models over a long period of time. The pandemic alternates periods of high and low infections, in a way…
This paper is devoted to the long-term dynamics of solutions to the Gurtin-MacCamy population model with a bistable birth function. We consider a one-parameter monotone family of initial distributions for the population such that for small…
Accurate epidemic forecasting requires models that account for the layered and heterogeneous nature of real social interactions. The basic reproduction number $\mathcal R_0$ calculated from models that assume homogeneous mixing or…
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…
Interactions between SARS-CoV-2 and the immune system during infection are complex. However, understanding the within-host SARS-CoV-2 dynamics is of enormous importance, especially when it comes to assessing treatment options. Mathematical…
We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient and recruitment rate. Initially, we conduct an extensive analysis of the autonomous scenario, covering aspects such as local and…
This paper carries out an analysis of the global properties of solutions of an in-host model of hepatitis C for general values of its parameters. A previously unknown stable steady state on the boundary of the positive orthant is exhibited.…
We investigate a stochastic individual-based model for the population dynamics of host-virus systems where the microbial hosts may transition into a dormant state upon contact with virions, thus evading infection. Such a contact-mediated…
The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon. If the basic reproduction number R0 is below unity, the disease-free equilibrium P0 is globally stable…
Threshold-driven models and game theory are two fundamental paradigms for describing human interactions in social systems. However, in mimicking social contagion processes, models that simultaneously incorporate these two mechanisms have…