The coronavirus pandemic has created a new awareness of epidemics, and insurance companies have been reminded to consider the risk related to infectious diseases. This paper extends the traditional multi-state models to include epidemic effects. The main idea is to specify the transition intensities in a Markov model such that the impact of contagion is explicitly present in the same way as in epidemiological models. Since we can study the Markov model with contagious effects at an individual level, we consider individual risk and reserves relating to insurance products, conforming with the standard multi-state approach in life insurance mathematics. We compare our notions with other but related notions in the literature and perform numerical illustrations.

Understanding the transfer of polychlorinated dibenzo-p-dioxins (PCDDs) and dibenzofurans (PCDFs) as well as polychlorinated biphenyls (PCBs) from oral exposure into cow’s milk is not purely an experimental endeavour, as it has produced a large corpus of theoretical work. This work consists of a variety of predictive toxicokinetic models in the realms of health and environmental risk assessment and risk management. Their purpose is to provide mathematical predictive tools to organise and integrate knowledge on the absorption, distribution, metabolism and excretion processes. Toxicokinetic models are based on more than 50 years of transfer studies summarised in part I of this review series. Here in part II, several of these models are described and systematically classified with a focus on their applicability to risk analysis as well as their limitations. This part of the review highlights the opportunities and challenges along the way towards accurate, congener-specific predictive models applicable to changing animal breeds and husbandry conditions.

In a previous article Saunders (1975) investigated the form of transition probabilities for a generalization of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The results of that investigation are given in terms of properties of exchangeable random variables and require that the process be in a particular initial state at time zero. This article removes the restriction on the initial state by using some properties of two sequences of jointly exchangeable variables. General results analogous to those obtained previously are shown to hold for general initial states.