Samuel Modée | Searcharxiv

arXiv2026

The Zombie Infection Model

We study a variant of the stochastic SIR model on graphs that has previously been introduced in the physics literature for modelling zombie outbreaks and here referred to as the Zombie Infection Model (ZIM). In this model, initially each node of a graph is either susceptible, infected or removed. As in the SIR model, a susceptible node becomes infected at rate $\lambda$ times the number of its infected neighbours. Moreover, in the ZIM, an infected node is removed at rate $1$ times the number of its susceptible neighbours. This process exhibits rich and sometimes counterintuitive behaviour. By combining various coupling techniques, we provide a rigorous mathematical analysis of the model, focusing on monotonicity properties and the probability of the infection spreading indefinitely. One of our main results is that this probability is monotone with respect to an increase of $\lambda$ for the process on trees, but that there are graphs of bounded degree for which it is continuous and yet not monotone. We also establish bounds on this probability for the process on general graphs, and derive more precise results for complete graphs, regular trees, and the $d$-dimensional integer lattice.

math.PR↗

arXiv2026

Multi-regime Markov-switching models with time-varying transition probabilities: An application to U.S. Treasury yields

This paper studies Markov-switching (MS) models with time-varying transition probabilities (TVTP) under various specifications of the transition probability matrix. In particular, we extend the two-regime common-variance setting of the Generalized Autoregressive Score (GAS) model from Bazzi et al. (2017) to the general $K$-regime case with regime-specific means and variances. Our study contains comprehensive Monte Carlo simulations and we develop an open-source R package, multiregimeTVTP, for data simulation, parameter estimation, evaluation of estimation performance, and forecasting robustness. We find that the regime means, variances, and transition probabilities are reliably recovered, whereas the TVTP driving coefficients are harder to identify. Another finding from our paper is that the GAS score coefficient appears to be statistically non-identifiable, due to a ridge in the likelihood surface linking it to the regime variance. In addition, we find that one-step point forecasts are remarkably robust to TVTP misspecification, whereas the filtered regime probabilities are accurately recovered under correct specification, so the value of correct specification lies in characterizing the regime dynamics rather than in short-horizon forecasting. An empirical application to U.S. Treasury zero-coupon yield changes (1961-2024) at four maturities shows that an exogenous specification driven by the lagged yield level provides the best fit among the considered models, attaining the lowest AIC at all four maturities and the lowest BIC at the short end of the yield curve. Overall, the evidence suggests that correctly specifying time-varying transition probabilities matters more for regime characterization and model fit than for short-horizon point forecasting.

stat.ME↗