Page 422 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
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MATHEMATICS IN BIOLOGY AND MEDICINE (MS-35)
References
[1] C. Barril, À. Calsina, S. Cuadrado, J. Ripoll: On the basic reproduction number in contin-
uously structured populations, submitted to Math. Meth. Appl. Sci., 2020.
[2] C. Barril, À. Calsina, J. Ripoll, A practical approach to R0 in continuous-time ecological
models. Math. Meth. Appl. Sci. 41 (18), 8432–8445, 2017.
[3] D. Breda, T. Kuniya, J. Ripoll, R. Vermiglio: Collocation of next-generation operators for
computing the basic reproduction number of structured populations, in preparation 2020.
[4] D. Breda, F. Florian, J. Ripoll, R. Vermiglio: Efficient numerical computation of the basic
reproduction number for structured populations, submitted to Int. J. Nonlin. Sci. Num.,
2019.
[5] C. Barril, À. Calsina J. Ripoll: On the reproduction number of a gut microbiota model, B.
Math. Biol., 79(11), 2727–2746, 2017.
The impact of herd behavior on stochastic competition model
Miljana Stankovic´, miksist90@gmail.com
Faculty of Sciences and Mathematics, University of Niš, Serbia
Coauthor: Miljana Jovanovic´
In this paper we extend the deterministic competition model with herd behavior and Allee ef-
fect by including environmental noise in the model. We prove that obtained stochastic model
has positive, global and bounded solution. Conditions under which system is stable in some
sense are established. We also apply our mathematical results to predict the time it takes for
populations of certain species to reach their equilibrium state.
Stochastic Hepatitis C model - conditions for disease extinction
Vuk Vujovic´, vukpharm@gmail.com
Faculty of Sciences and Mathematics, University of Niš, Serbia
Coauthor: Marija Krstic´
Hepatitis C is an infectious liver disease caused by the Hepatitis C virus and transmitted exclu-
sively by infected person’s blood. There are many papers in the literature which consider spread
of Hepatitis C. In some of them infected persons are divided in two classes: acute and chronic
persons, but we construct our stochastic model on basis of the deterministic one which takes
into account the isolation stage of infection, too. Hence, we obtain, five-state stochastic model
by using system of stochastic differential equations of Ito type. This model better describes vari-
ability and uncertainty which may manifest through the contact between persons in population.
Also stochastic model is constructed on such way, that inherits the disease free equilibrium
point of deterministic model. In this presentation the conditions for coefficient of stochastic
systems that provide stability in probability of disease free equilibrium state are shown. On the
other words, it means, that under these conditions Hepatitis C will die out in population. Our
420
References
[1] C. Barril, À. Calsina, S. Cuadrado, J. Ripoll: On the basic reproduction number in contin-
uously structured populations, submitted to Math. Meth. Appl. Sci., 2020.
[2] C. Barril, À. Calsina, J. Ripoll, A practical approach to R0 in continuous-time ecological
models. Math. Meth. Appl. Sci. 41 (18), 8432–8445, 2017.
[3] D. Breda, T. Kuniya, J. Ripoll, R. Vermiglio: Collocation of next-generation operators for
computing the basic reproduction number of structured populations, in preparation 2020.
[4] D. Breda, F. Florian, J. Ripoll, R. Vermiglio: Efficient numerical computation of the basic
reproduction number for structured populations, submitted to Int. J. Nonlin. Sci. Num.,
2019.
[5] C. Barril, À. Calsina J. Ripoll: On the reproduction number of a gut microbiota model, B.
Math. Biol., 79(11), 2727–2746, 2017.
The impact of herd behavior on stochastic competition model
Miljana Stankovic´, miksist90@gmail.com
Faculty of Sciences and Mathematics, University of Niš, Serbia
Coauthor: Miljana Jovanovic´
In this paper we extend the deterministic competition model with herd behavior and Allee ef-
fect by including environmental noise in the model. We prove that obtained stochastic model
has positive, global and bounded solution. Conditions under which system is stable in some
sense are established. We also apply our mathematical results to predict the time it takes for
populations of certain species to reach their equilibrium state.
Stochastic Hepatitis C model - conditions for disease extinction
Vuk Vujovic´, vukpharm@gmail.com
Faculty of Sciences and Mathematics, University of Niš, Serbia
Coauthor: Marija Krstic´
Hepatitis C is an infectious liver disease caused by the Hepatitis C virus and transmitted exclu-
sively by infected person’s blood. There are many papers in the literature which consider spread
of Hepatitis C. In some of them infected persons are divided in two classes: acute and chronic
persons, but we construct our stochastic model on basis of the deterministic one which takes
into account the isolation stage of infection, too. Hence, we obtain, five-state stochastic model
by using system of stochastic differential equations of Ito type. This model better describes vari-
ability and uncertainty which may manifest through the contact between persons in population.
Also stochastic model is constructed on such way, that inherits the disease free equilibrium
point of deterministic model. In this presentation the conditions for coefficient of stochastic
systems that provide stability in probability of disease free equilibrium state are shown. On the
other words, it means, that under these conditions Hepatitis C will die out in population. Our
420
