Stochastic infectivity models to analyse the dynamics of the spread

XXV Simposio Internacional de Estadística 2015
Armenia, Colombia, 5, 6, 7 y 8 de Agosto de 2015
Stochastic infectivity models to analyse the dynamics of the
spread of a disease
Liliana Blanco1,a , Viswanathan Arunachalam1,b
1 Departamento
de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia
Resumen
Stochastic Modeling of diseases of epidemics is an important tool in public health system, since
stochastic models offer a tractable information to analyze the uncertainty outbreaks of epidemic
dynamics and help to control spread of the diseases. We assume that at time origin there are infinitely
many susceptible individuals. A susceptible may be infected at time t > 0, after which it is classified as
infected. It is assumed that the random variable denoting the time between two successive infections
is exponentially distributed and that infections are due to a source of infection from outside of the
population. Our interest is analysing the statistical characteristics of the total force of infectivity
f (t) present in the population at any time t . In this paper we propose an endemic and an epidemic
stochastic models to describe the dynamics of a disease in a large population of susceptible individual.
The core of the models is the force of the infection. Each of the infected individual contributes a
non stationary term to the total force of the infection. This comprises of a discrete jump at the
instant of infection which could be deterministic or random and a response function. The statistical
characteristics of the number of infected are obtained from the conditional intensity function.
Palabras clave: Stochastic models, Epidemics, Infectivity function.
a.
b.
E-mail: lblancoc@unal.edu.co
E-mail: varunachalam@unal.edu.co
1