Birth and death process in epidemiology.
Keywords:
Epidemiology, Stochastic Processes, Mathematical Modeling
Abstract
In this work, we present a general ideas in birth-death processes,
which are a particular kind of stochastic process. We
present birth-death process applied for some biological examples.
We present a birth-death model used for modeling the
behaivoir in the number of infected individuals as an epidemiological
problem. This process has a finite transition probabilities
matrix, which all their entries are constants. The last part
of the work, we present a infinite matrix and some ideas about
the solution on this problem, adapted to the epidemiological
example deal in the previous section.
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References
Allen, E., Allen, L., Arciniega, A., Greenwood, P., 2008. Construction of equivalent
stochastic dierential equation models. Stochastic Analysis and Applications
26, 274–297.
Allen, L., 2010. Stochastic Processes wiht Applications to Biology, 1st Edition.
CRC Press, Lubbock.
Andersson, H., Britton, T., 2000. Stochastic Epidemic Models and Their Statistical
Analysis, 1st Edition. Springer-Verlag, New York.
Brauer, F., Castillo-Ch´avez, C., De la Pava, E., Barley, K., Castillo-Garsow,
C., Chowell, D., Espinoza, B., Gonz´alez Parra, P., Hern´andez Su´arez, C.,
Moreno, V., 2014. Modelos de la propagaci´on de enfermedades infecciosas,
1st Edition. Universidad Aut´onoma de Occidente, Cali.
Brauer, F., van den Driessche, P., Wu, J., 2008. Mathematical Epidemiology,
1st Edition. Springer-Verlag, Berlin.
Doob, J., 1990. Stochastic Processes, 1st Edition. John Wiley and Sons, New
York.
Doss, C., Suchard, M., Holmes, I., Kato-Maeda, M., Minin, V., 2013. Fitting
birth-death processes to panel data with applications to bacterial dna fingerprinting.
The Annals of Applied Statistics 7(4), 2315–2355.
Eslahchi, C., Movahedi, F., 2012. Calculation of transition probabilities in the
birth and death markov process in the epidemic model. Mathematical and
Computer Modelling 55, 810–815.
Hansson, D., 2013. Birth and Death Models with time dependent rates applied
to virus phylogenesis. Stockholms Universitet, Stockholm.
Hern´andez-Su´arez, C., Castillo-Chavez, C., 1999. A basic result on the integral
for birth-death markov process. Mathematical Biosciences 161, 95–104.
Ho, L., Xu, J., Crawford, F., Minin, V., Suchard, M., 2018. Birth/birth-death
processes and theier computable transition probabilities with biological applications.
J. Math. Biol. 76(4), 911–944.
Jim´enez-Mungu´ıa, R., 2017. Modelaci´on de procesos ca´oticos mediante operadores
de Toeplitz. Universidad Nacional Aut´onoma de M´exico, M´exico.
Novazhilov, A.S., K. G., Koonin, E., 2006. Biological applications of the theory
of birth-and-death processes. Briefings in Bioinformatics 7(1), 70–85.
zu Donna, H., Pineda-Krch, M., 2010. Fitting parameters of stochastic birthdeath
models to metapopulation data. Theoretical Population Biology 78,
71–76.
stochastic dierential equation models. Stochastic Analysis and Applications
26, 274–297.
Allen, L., 2010. Stochastic Processes wiht Applications to Biology, 1st Edition.
CRC Press, Lubbock.
Andersson, H., Britton, T., 2000. Stochastic Epidemic Models and Their Statistical
Analysis, 1st Edition. Springer-Verlag, New York.
Brauer, F., Castillo-Ch´avez, C., De la Pava, E., Barley, K., Castillo-Garsow,
C., Chowell, D., Espinoza, B., Gonz´alez Parra, P., Hern´andez Su´arez, C.,
Moreno, V., 2014. Modelos de la propagaci´on de enfermedades infecciosas,
1st Edition. Universidad Aut´onoma de Occidente, Cali.
Brauer, F., van den Driessche, P., Wu, J., 2008. Mathematical Epidemiology,
1st Edition. Springer-Verlag, Berlin.
Doob, J., 1990. Stochastic Processes, 1st Edition. John Wiley and Sons, New
York.
Doss, C., Suchard, M., Holmes, I., Kato-Maeda, M., Minin, V., 2013. Fitting
birth-death processes to panel data with applications to bacterial dna fingerprinting.
The Annals of Applied Statistics 7(4), 2315–2355.
Eslahchi, C., Movahedi, F., 2012. Calculation of transition probabilities in the
birth and death markov process in the epidemic model. Mathematical and
Computer Modelling 55, 810–815.
Hansson, D., 2013. Birth and Death Models with time dependent rates applied
to virus phylogenesis. Stockholms Universitet, Stockholm.
Hern´andez-Su´arez, C., Castillo-Chavez, C., 1999. A basic result on the integral
for birth-death markov process. Mathematical Biosciences 161, 95–104.
Ho, L., Xu, J., Crawford, F., Minin, V., Suchard, M., 2018. Birth/birth-death
processes and theier computable transition probabilities with biological applications.
J. Math. Biol. 76(4), 911–944.
Jim´enez-Mungu´ıa, R., 2017. Modelaci´on de procesos ca´oticos mediante operadores
de Toeplitz. Universidad Nacional Aut´onoma de M´exico, M´exico.
Novazhilov, A.S., K. G., Koonin, E., 2006. Biological applications of the theory
of birth-and-death processes. Briefings in Bioinformatics 7(1), 70–85.
zu Donna, H., Pineda-Krch, M., 2010. Fitting parameters of stochastic birthdeath
models to metapopulation data. Theoretical Population Biology 78,
71–76.
Published
2019-01-05
How to Cite
Ávila Pozos, R., Cruz Castillo, R., & Jiménez-Munguía, R. R. (2019). Birth and death process in epidemiology. Pädi Boletín Científico De Ciencias Básicas E Ingenierías Del ICBI, 6(12), 86-90. https://doi.org/10.29057/icbi.v6i12.3437
Section
Research papers
