Related papers: An eco-epidemiological model with general function…
The comprehension of how local interactions arise in global collective behavior is of utmost importance in both biological and physical research. Traditional agent-based models often rely on static rules that fail to capture the dynamic…
A generalisation of the Susceptible-Infectious model is made to include a time-dependent transmission rate, which leads to a close analytical expression in terms of a logistic function. The solution can be applied to any continuous function…
Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state…
It is essential to understand the dynamics of epidemics in the presence of coexisting pathogens. There are various phenomenon that can effect the dynamics. In this paper, we formulate a mathematical model using different assumptions to…
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…
Consider the coupling of $2$ evolution equations, each generating a global process. We prove that the resulting system generates a new global process. This statement can be applied to differential equations of various kinds. In particular,…
We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…
Ecosystems are formed by networks of species and their interactions. Traditional models of such interactions assume a constant interaction strength between a given pair of species. However, there is often significant trait variation among…
We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behaviour in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of…
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…
We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing…
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…
Much traditional statistical modelling assumes that the outcome variables of interest are independent of each other when conditioned on the explanatory variables. This assumption is strongly violated in the case of infectious diseases,…
We introduce a new model for large scale evolution and extinction in which species are organized into food chains. The system evolves by two processes: origination/speciation and extinction. In the model, extinction of a given species can…
An interesting inference drawn by some Covid-19 epidemiological models is that there exists a proportion of the population who are not susceptible to infection -- even at the start of the current pandemic. This paper introduces a model of…
We present a systematic review of some basic results on the derivation of classical epidemiological models from simple agent-based dynamics. The evolution of large populations is coupled with the dynamics of the contact distribution,…
We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties…
Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species.…
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA)and computer simulations. The MFA results a…