Projects per year
Abstract
In this paper we look at the two dimensional stochastic differential equation (SDE) susceptibleinfectedsusceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique nonnegative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique nonnegative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values.
Original language  English 

Pages (fromto)  218238 
Number of pages  21 
Journal  Applied Mathematics and Computation 
Volume  276 
Early online date  7 Jan 2016 
DOIs  
Publication status  Published  5 Mar 2016 
Keywords
 two dimensional SIS epidemic model
 demographic stochasticity
 varying population size
 extinction
 stochastic differential equation
 Brownian motion
Profiles
Projects
 4 Finished

Numerical Analysis of Stochastic Differential Equations: New Challenges
1/10/15 → 30/09/17
Project: Research Fellowship


Epsrc Doctoral Training Grant  Liang, Yanfeng
Greenhalgh, D., Mao, X. & Liang, Y.
EPSRC (Engineering and Physical Sciences Research Council)
1/10/12 → 3/10/16
Project: Research Studentship  Internally Allocated