Stochastic Monotonicity and Continuity Properties of the Extinction Time of Bellman–harris Branching Processes: an Application to Epidemic Modelling
نویسندگان
چکیده
The aim of this paper is to study the stochastic monotonicity and continuity properties of the extinction time of Bellman–Harris branching processes depending on their reproduction laws. Moreover, we show their applications in an epidemiological context, obtaining an optimal criterion to establish the proportion of susceptible individuals in a given population that must be vaccinated in order to eliminate an infectious disease. First the spread of infection is modelled by a Bellman–Harris branching process. Finally, we provide a simulation-based method to determine the optimal vaccination policies.
منابع مشابه
Stochastic monotonicity and continuity properties of functions defined on Crump–Mode–Jagers branching processes, with application to vaccination in epidemic modelling
FRANK BALL, MIGUEL GONZÁLEZ, RODRIGO MARTÍNEZ and MAROUSSIA SLAVTCHOVA-BOJKOVA School of Mathematical Sciences, The University of Nottingham, Nottingham NG7 2RD, United Kingdom. E-mail: [email protected] Department of Mathematics, University of Extremadura, Avda, Elvas s/n, 06071-Badajoz, Spain. E-mail: [email protected]; [email protected] Faculty of Mathematics and Informatics, Sofia ...
متن کاملApplication of Stochastic Optimal Control, Game Theory and Information Fusion for Cyber Defense Modelling
The present paper addresses an effective cyber defense model by applying information fusion based game theoretical approaches. In the present paper, we are trying to improve previous models by applying stochastic optimal control and robust optimization techniques. Jump processes are applied to model different and complex situations in cyber games. Applying jump processes we propose some m...
متن کاملAPPLICATION OF THE BELLMAN AND ZADEH'S PRINCIPLE FOR IDENTIFYING THE FUZZY DECISION IN A NETWORK WITH INTERMEDIATE STORAGE
In most of the real-life applications we deal with the problem of transporting some special fruits, as banana, which has particular production and distribution processes. In this paper we restrict our attention to formulating and solving a new bi-criterion problem on a network in which in addition to minimizing the traversing costs, admissibility of the quality level of fruits is a main objecti...
متن کاملAn Introduction to Stochastic Epidemic Models
A brief introduction to the formulation of various types of stochastic epidemic models is presented based on the well-known deterministic SIS and SIR epidemic models. Three different types of stochastic model formulations are discussed: discrete time Markov chain, continuous time Markov chain and stochastic differential equations. Properties unique to the stochastic models are presented: probab...
متن کاملIdentifiability of Age-Dependent Branching Processes from Extinction Probabilities and Number Distributions
Consider an age-dependent, single-species branching process defined by a progeny number distribution, and a lifetime distribution associated with each independent particle. In this paper, we focus on the associated inverse problem where one wishes to formally solve for the progeny number distribution or the lifetime distribution that defines the Bellman-Harris branching process. We derive resul...
متن کامل