A stochastic model for the spread of an SIS epidemic among a population consisting of N individuals, each having heterogeneous infectiousness and/or susceptibility, is considered and its behavior is analyzed under the practically relevant situation when N is small. The model is formulated as a finite time-homogeneous continuous-time Markov chain X. Based on an appropriate labeling of states, we first construct its infinitesimal rate matrix by using an iterative argument, and we then present an algorithmic procedure for computing steady-state measures, such as the number of infected individuals, the length of an outbreak, the maximum number of infectives, and the number of infections suffered by a marked individual during an outbreak. The time till the epidemic extinction is characterized as a phase-type random variable when there is no external source of infection, and its Laplace-Stieltjes transform and moments are derived in terms of a forward elimination backward substitution solution. The inverse iteration method is applied to the quasi-stationary distribution of X, which provides a good approximation of the process X at a certain time, conditional on non-extinction, after a suitable waiting time. The basic reproduction number R-0 is defined here as a random variable, rather than an expected value

Bacterial transmission from contaminated surfaces via hand contact plays a critical role in disease spread. However, the fomite‐to‐finger transfer efficiency of microorganisms during multiple sequential surface contacts with and without gloves has not been formerly investigated. We measured the quantity of Escherichia coli on fingertips of participants after one‐to‐eight sequential contacts with inoculated plastic coupons with and without nitrile gloves. A Bayesian approach was used to develop a mechanistic model of pathogen accretion to examine finger loading as a function of the difference between E. coli on surfaces and fingers. We used the model to determine the coefficient of transfer efficiency (λ), and influence of swabbing efficiency and finger area. Results showed λ for bare skin was higher (49%, 95%CI=32‐72%) than for gloved hands (30%, CI=17‐49%). Microbial load tended towards a dynamic equilibrium after four and six contacts for gloved hands and bare skin, respectively. Individual differences between volunteers’ hands had a negligible effect compared with use of gloves (p<0.01). Gloves reduced loading by 4.7% (CI=‐12%‐21%) over bare skin contacts whilst 20% of participants accrued more microorganisms on gloved hands. This was due to poor fitting, which created a larger finger surface area than bare hands.

We continue here the work initiated in [13], and analyse an SIR epidemic model for the spread of an epidemic among the members of a small population of N individuals, defined in terms of a continuous-time Markov chain X. We propose a structure by levels and sub-levels of the state space of the process X, and present two different orders, Orders A and B, for states within each sub-level, which are related to a matrix and a scalar formalism, respectively, when developing our analysis. Stochastic descriptors regarding the length and size of an outbreak, the maximum number of individuals simultaneously infected during an outbreak, the fate of a particular individual within the population, and the number of secondary cases caused by a certain individual until he recovers, are deeply analysed. Our approach is illustrated by carrying out a set of numerical results regarding the spread of the nosocomial pathogen Methicillin-resistant Staphylococcus Aureus among the patients within an intensive care unit. In this application, our interest is in analysing the effectiveness of control strategies (the isolation of the patient initiating the outbreak and the proper room configuration of the intensive care unit) that intrinsically introduce heterogeneities among the members of the population. (C) 2015 Elsevier Inc. All rights reserved.

Cytokines elicit pleiotropic and non-redundant activities despite strong overlap in their usage of receptors, JAKs and STATs molecules. We use IL-6 and IL-27 to ask how two cytokines activating the same signaling pathway have different biological roles. We found that IL-27 induces more sustained STAT1 phosphorylation than IL-6, with the two cytokines inducing comparable levels of STAT3 phosphorylation. Mathematical and statistical modeling of IL-6 and IL-27 signaling identified STAT3 binding to GP130, and STAT1 binding to IL-27Rα, as the main dynamical processes contributing to sustained pSTAT1 levels by IL-27. Mutation of Tyr613 on IL-27Rα decreased IL-27-induced STAT1 phosphorylation by 80% but had limited effect on STAT3 phosphorgylation. Strong receptor/STAT coupling by IL-27 initiated a unique gene expression program, which required sustained STAT1 phosphorylation and IRF1 expression and was enriched in classical Interferon Stimulated Genes. Interestingly, the STAT/receptor coupling exhibited by IL-6/IL-27 was altered in patients with systemic lupus erythematosus (SLE). IL-6/IL-27 induced a more potent STAT1 activation in SLE patients than in healthy controls, which correlated with higher STAT1 expression in these patients. Partial inhibition of JAK activation by sub-saturating doses of Tofacitinib specifically lowered the levels of STAT1 activation by IL-6. Our data show that receptor and STATs concentrations critically contribute to shape cytokine responses and generate functional pleiotropy in health and disease.

It is often possible to model the dynamics of biological systems as a series of discrete transitions between a finite set of observable states (or compartments). When the residence times in each state, or inter-event times more generally, are exponentially distributed, then one can write a set of ordinary differential equations, which accurately describe the evolution of mean quantities. Non-exponential inter-event times can also be experimentally observed, but are more difficult to analyse mathematically. In this paper, we focus on the computation of first passage events and their probabilities in biological systems with non-exponential inter-event times. We show, with three case studies from Molecular Immunology, Virology and Epidemiology, that significant errors are introduced when drawing conclusions based on the assumption that inter-event times are exponentially distributed. Our approach allows these errors to be avoided with the use of phase-type distributions that approximate arbitrarily distributed inter-event times.