Related papers: On the basic reproduction number in continuously s…
In this paper, we consider the infection-age-dependent Kermack--McKendrick model in which host individuals are distributed in a continuous state space. To provide a mathematical foundation for the heterogeneous model, we develop a…
In this paper we present a new modelling framework combining replicator dynamics (which is the standard model of frequency dependent selection) with the model of an age-structured population. The new framework allows for the modelling 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…
We consider age-structured models with an imposed refractory period between births. These models can be used to formulate alternative population control strategies to China's one-child policy. By allowing any number of births, but with an…
The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs…
This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under…
We construct a pathwise formulation for a multi-type age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational…
For nearly a century, the initial reproduction number (R0) has been used as a one number summary to compare outbreaks of infectious disease, yet there is no `standard' estimator for R0. Difficulties in estimating R0 arise both from how a…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
The population dynamics that evolves in the radial symmetric geometry is investigated. The nonlinear reaction-diffusion model, which depends on population density, is employed as the governing equation for this system. The approximate…
We consider an exactly solvable model of branching random walk with random selection, which describes the evolution of a population with $N$ individuals on the real line. At each time step, every individual reproduces independently, and its…
Accurate estimates of the reproduction ratio are crucial to project infectious disease epidemic evolution and guide public health response. Here, we prove that estimates of the reproduction ratio based on inference from surveillance data…
A wide range of infectious diseases are both vertically and horizontally transmitted. Such diseases are spatially transmitted via multiple species in heterogeneous environments, typically described by complex meta-population models. The…
We develop a class of nonlocal delay Reaction-Diffusion (RD) models in a circular domain. Previous modeling efforts include RD population models with respect to one-dimensional unbounded domain, unbounded strip and rectangular spatial…
We consider a two-patches SIR model where communication occurs thru commuters, distinguishing explicitly permanently resident populations from commuters populations. We give an explicit formula of the reproduction number, and show how the…
For synthesising star clusters and whole galaxies, stellar populations need to be modelled by a set of four functions that define their initial distribution of stellar masses and of the orbital properties of their binary-star populations.…
Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R0). First we solved a generic, deterministic compartmental model of re-infection…
Natural rivers connect to each other to form networks. The geometric structure of a river network can significantly influence spatial dynamics of populations in the system. We consider a process-oriented model to describe population…
We consider random recursive trees that are grown via community modulated schemes that involve random attachment or degree based attachment. The aim of this paper is to derive general techniques based on continuous time embedding to study…
A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family…