Page 513 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 513
MULTISCALE MODELING AND METHODS: APPLICATION IN ENGINEERING,
BIOLOGY AND MEDICINE (MS-80)
In order to study the asymptotic behaviour of the flow as ε tends to zero we apply the multi-
ple scale convergence technique for reiterated homogenization problems ([1]). The assumption
m ≥ 2 raises several technical difficulties and leads to a new type of divergence free conditions
for the limit velocity which play a crucial role in the derivation of the limit problem.
Finally we prove that the limit velocity and pressure (v0, p0) and angular micro-rotation field
Z0 solve a totally decoupled system of elliptic variational inequality on one hand and elliptic
partial differential equation on the other hand, where the time variable appears as a parameter.
Furthermore v0, p0 and Z0 are uniquely determined through auxiliary well-posed problems.
[joint work with M.Boukrouche and F.Ziane]
References
[1] G. Allaire, M. Briane. Multiscale convergence and reiterated homogenisation. Proc. Roy.
Soc. Edinb. vol. 126, 297-342, 1996.
[2] A.C. Eringen. Theory of micropolar fluids. Journal of Mathematics and Mechanics, vol.
16(1), 1-18, 1966.
[3] H. Fujita. Flow problems with unilateral boundary conditions. Leçons au Collège de
France, 1993.
Modeling the evolution of COVID-19 in Lithuania
Olga Štikoniene˙, olga.stikoniene@mif.vu.lt
Vilnius University, Institute of Applied Mathematics, Lithuania
Coauthors: Barbora Šnaraite˙, Remigijus Leipus
Models based on data analysis are being developed for the spread of the COVID-19 epidemic.
A mathematically based methodology was developed for the analysis and assessment of the
spread of potential epidemics and their consequences. It has the potential of becoming one of
the tools of the state to manage crisis situations caused by epidemics, especially in the early
phase of epidemic spread. We present the model for the spread of COVID-19 in Lithuania for
the period March—December, 2020. Our approach is based on the generalized SEIR model
which is derived from a set of ordinary differential equations that incorporates the transition
rates at which population moves from one compartment to another. It is important to note that
in the initial phase of the virus spread, when the data were very limited, it was necessary to rely
on the experience of other countries and adapt the used epidemiological models to Lithuania.
As the modeling results show, in the early phase the generalized SEIR model showed rather
accurate forecasts. Later it became possible to construct more accurate and flexible models
due to a wide range of data. As with many mathematical-statistical models, the accuracy of
prediction relies heavily on the quality of the available data and the level of model abstraction.
511
BIOLOGY AND MEDICINE (MS-80)
In order to study the asymptotic behaviour of the flow as ε tends to zero we apply the multi-
ple scale convergence technique for reiterated homogenization problems ([1]). The assumption
m ≥ 2 raises several technical difficulties and leads to a new type of divergence free conditions
for the limit velocity which play a crucial role in the derivation of the limit problem.
Finally we prove that the limit velocity and pressure (v0, p0) and angular micro-rotation field
Z0 solve a totally decoupled system of elliptic variational inequality on one hand and elliptic
partial differential equation on the other hand, where the time variable appears as a parameter.
Furthermore v0, p0 and Z0 are uniquely determined through auxiliary well-posed problems.
[joint work with M.Boukrouche and F.Ziane]
References
[1] G. Allaire, M. Briane. Multiscale convergence and reiterated homogenisation. Proc. Roy.
Soc. Edinb. vol. 126, 297-342, 1996.
[2] A.C. Eringen. Theory of micropolar fluids. Journal of Mathematics and Mechanics, vol.
16(1), 1-18, 1966.
[3] H. Fujita. Flow problems with unilateral boundary conditions. Leçons au Collège de
France, 1993.
Modeling the evolution of COVID-19 in Lithuania
Olga Štikoniene˙, olga.stikoniene@mif.vu.lt
Vilnius University, Institute of Applied Mathematics, Lithuania
Coauthors: Barbora Šnaraite˙, Remigijus Leipus
Models based on data analysis are being developed for the spread of the COVID-19 epidemic.
A mathematically based methodology was developed for the analysis and assessment of the
spread of potential epidemics and their consequences. It has the potential of becoming one of
the tools of the state to manage crisis situations caused by epidemics, especially in the early
phase of epidemic spread. We present the model for the spread of COVID-19 in Lithuania for
the period March—December, 2020. Our approach is based on the generalized SEIR model
which is derived from a set of ordinary differential equations that incorporates the transition
rates at which population moves from one compartment to another. It is important to note that
in the initial phase of the virus spread, when the data were very limited, it was necessary to rely
on the experience of other countries and adapt the used epidemiological models to Lithuania.
As the modeling results show, in the early phase the generalized SEIR model showed rather
accurate forecasts. Later it became possible to construct more accurate and flexible models
due to a wide range of data. As with many mathematical-statistical models, the accuracy of
prediction relies heavily on the quality of the available data and the level of model abstraction.
511
