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We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected with the rate $\lambda$ when contacting $m$ infective individual(s) simultaneously, and an…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
Let $X$ be a continuous-time strongly mixing or weakly dependent process and $T$ a renewal process independent of $X$ with inter-arrival times $\tau$. We show general conditions under which the sampled process $(X_{T_i},T_i-T_{i-1})^{\top}$…
Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
A general stochastic model for susceptible -> infective -> recovered (SIR) epidemics in non homogeneous populations is considered. The heterogeneity is a very important aspect here since it allows more realistic but also more complex…
We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting…
Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
A standard quantitative method to access credit risk employs a factor model based on joint multivariate normal distribution properties. By extending a one-factor Gaussian copula model to make a more accurate default forecast, this paper…
The ever-changing world of disease study heavily relies on mathematical models. They are key in finding and controlling infectious diseases. We aim to explore these mathematical tools used for studying disease spread in biology. The SEIR…
Retrospective causal questions ask what would have happened to an observed individual had they received a different treatment. We study the problem of estimating $\mu(x,y)=\mathbb{E}[Y(1)\mid X=x,Y(0)=y]$, the expected counterfactual…
In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be `cured'. The population is thus a mixture of two subpopulations: the one of cured subjects, and the one…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
Couplings in complex real-world systems are often nonlinear and scale-dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
Survival analysis, or time-to-event modelling, is a classical statistical problem that has garnered a lot of interest for its practical use in epidemiology, demographics or actuarial sciences. Recent advances on the subject from the point…
Filtering has had a profound impact as a device of perceiving information and deriving agent expectations in dynamic economic models. For an abstract economic system, this paper shows that the foundation of applying the filtering method…
We investigate a specific reaction-diffusion system that admits a monostable pulled front propagating at constant critical speed. When a small parameter changes sign, the stable equilibrium behind the front destabilizes, due to essential…