Related papers: Mathematical analysis of a two-strain disease mode…
We present a model for obligated mutualistic associations, in which two transmissible diseases are allowed to infect just one population. As the general model proves too hard to be fully analytically investigated, some special cases are…
We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al.…
Using a probability of novel encounter derived from a physical model, we augment the SIR compartmental model for disease spread. Scenarios with the same initial trajectories and identical $R_0$ values can diverge greatly depending on the…
Compartmental epidemic models with dynamics that evolve over a graph network have gained considerable importance in recent years but analysis of these models is in general difficult due to their complexity. In this paper, we develop two…
We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…
This article conducts an in-depth investigation of a new spatio-temporal model for the cocaine-heroin epidemiological model with vital dynamics, incorporating the Laplacian operator. The study rigorously establishes the existence,…
In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible-Infected-Susceptible) epidemic model recently proposed in [A. Gray et al., SIAM. J. Appl. Math., 71 (2011), 876-902]. We…
The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the…
We consider the standard three-component differential equation model for the growth of an HIV virion population in an infected host in the absence of drug therapy. The dynamical properties of the model are determined by the set of values of…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
An epidemic spreading in a network calls for a decision on the part of the network members: They should decide whether to protect themselves or not. Their decision depends on the trade-off between their perceived risk of being infected and…
Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and…
Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains,…
We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed…
A new mathematical model for the dynamics of prion proliferation involving an ordinary differential equation coupled with a partial integro-differential equation is analyzed, continuing earlier work. We show the well-posedness of this…
The paper deals with the setting where two viruses (say virus 1 and virus 2) coexist in a population, and they are not necessarily mutually exclusive, in the sense that infection due to one virus does not preclude the possibility of…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
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…