Related papers: The network-level reproduction number and extincti…
Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations…
We adapt the article of Forien, Pang, Pardoux and Zotsa: Arxiv preprint Arxiv2210.04667(2022), on epidemic models with varying infectivity and waning immunity, to incorporate the memory of the last infection. To this end, we introduce a…
We study the influence of global, local and community-level risk perception on the extinction probability of a disease in several models of social networks. In particular, we study the infection progression as a…
Reproduction numbers, like the basic reproduction number $\mathcal{R}_0$, play an important role in the analysis and application of dynamic models, including contagion models and ecological population models. One difficulty in deriving…
The basic reproduction number R0 is a concept which originated in population dynamics, mathematical epidemiology, and ecology and is closely related to the mean number of children in branching processes.We offer below three new…
To investigate the combined effects of drug resistance, seasonality and vector-bias, we formulate a periodic two-strain reaction-diffusion model. It is a competitive system for resistant and sensitive strains, but the single-strain…
In this paper, we propose a realistic mathematical model taking into account the mutual interference among the interacting populations. This model attempts to describe the control (vaccination) function as a function of the number of…
In the absence of other tools, monitoring the effects of protective measures, including social distancing and forecasting the outcome of outbreaks is of immense interest. Real-time data is noisy and very often hampered by systematic errors…
Vector-borne diseases with reservoir cycles are complex to understand because new infections come from contacts of the vector with humans and different reservoirs. In this scenario, the basic reproductive number $\mathcal{R}^h_0$ of the…
We study some simple models of disease transmission on small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both. The resulting models display epidemic behavior…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
Epidemic models often reflect characteristic features of infectious spreading processes by coupled non-linear differential equations considering different states of health (such as Susceptible, Infected, or Recovered). This compartmental…
Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…
We study species abundance in the empirical plant-pollinator mutualistic networks exhibiting broad degree distributions, with uniform intra-group competition assumed, by the Lotka-Volterra equation. The stability of a fixed point is found…
Cities have long served as nucleating centers for human development and advancement. Cities have facilitated the spread of both human creativity and human disease, and at the same time, efforts to minimize the spread of disease have…
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…
We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in…
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
We study a generic reaction-diffusion model for single-species population dynamics that includes reproduction, death, and competition. The population is assumed to be confined in a refuge beyond which conditions are so harsh that they lead…