TY  - JOUR
AB  - The aim of this paper is to develop an integrated model of pandemics to study effectiveness of public health policies in controlling infections, taking into account the response of people to these policies. A causal framework is developed to explain the interaction of disease prevalence, containment policies and population response with the status of the pandemic. An information-related framework is applied to analyse the design and conduct of public policies and the response of individuals to them. In this framework, the government applies a Markov decision process to decide on optimal containment polices. Using risk perception into a cost-benefit analysis, we explain how people decide to respond to public health policies. These frameworks are introduced into an SIR model to analyse how interaction between public health policies and individuals’ response to these policies affect dynamics of disease transmission. The model is calibrated and simulated for the province of Ontario in Canada. The results show that government policies to control contact numbers and people response to policies, effectively decrease the rate of transmission within age-groups. Our findings highlight that risk perception plays a significant role in the response of people to policies and outcomes of the pandemic.
AU  - Haskuee, M.B.*
AU  - Efendiyev, M.A.
AU  - Murty, K.K.*
C1  - 73291
C2  - 56821
SP  - 419-457
TI  - Containment policies, behaviour and dynamics of the pandemic.
JO  - Adv. Math. Sci. Appl.
VL  - 33
IS  - 2
PY  - 2024
SN  - 1343-4373
ER  - 

TY  - JOUR
AB  - The work deals with the easily verifiable necessary conditions of the preser-vation of the nonnegativity of the solutions of a system of parabolic equations in the case of the double scale anomalous diffusion when the fractional Laplacian is added to the negative Laplace operator raised to another fractional power in the space of two dimen-sions. Such necessary conditions are extremely important for the applied analysis society because they impose the necessary form of the system of equations that must be studied mathematically.
AU  - Efendiyev, M.A.
AU  - Vougalter, V.*
C1  - 66433
C2  - 53179
SP  - 197-206
TI  - On the necessary conditions for preserving the nonnegative cone: Double scale anomalous diffusion.
JO  - Adv. Math. Sci. Appl.
VL  - 31
IS  - 1
PY  - 2022
SN  - 1343-4373
ER  - 

TY  - JOUR
AB  - In this paper, we consider deterministic, continuous, nonlocal models for the mitochondrial permeability transition, i.e. mitochondrial swelling. Based on seminal papers [1], [2], [3], [5] and the book [4], in which ODE-PDE and PDE-PDE local models for the swelling of mitochondria have been considered, we suggest here new nonlocal models for this process. This new nonlocal deterministic continuous model for mitochondrial swelling scenario contains nonlocal diffusion, nonlocal chemotaxis, as well as nonlocal source term. We would like to especially emphasize that some of the new nonlocal models that we consider in this paper do not have local counterparts in the literature.
AU  - Efendiyev, M.A.
AU  - Muradova, A.*
AU  - Muradov, N.*
AU  - Zischka, H.
C1  - 64857
C2  - 51915
SP  - 377-385
TI  - Local vs nonlocal models for mitochondria swelling.
JO  - Adv. Math. Sci. Appl.
VL  - 30
IS  - 2
PY  - 2021
SN  - 1343-4373
ER  - 

TY  - JOUR
AU  - Efendiyev, M.A.
AU  - Zhigun, A.*
C1  - 30579
C2  - 34025
SP  - 437-460
TI  - On a global uniform pull-back attractor of a class of PDEs with degenerate diffusion and chemotaxis.
JO  - Adv. Math. Sci. Appl.
VL  - 23
IS  - 2
PY  - 2013
SN  - 1343-4373
ER  - 

TY  - JOUR
AB  - We consider some elliptic semilinear boundary value problem set either in the quadrant {χ1 >0} x {χN > 0} or in the halfspace {χ1 >0} if RN , and we classify the asymptotoc behavior of the solution as χ1 -> +. The dimension N is taken up to 5 or up to 4, according to the case, and the nonlinearity is of dissipative type. The proof are a combination of techniques borrowed from dynamical systems (to construct a global attractor of solutions) and from partial differential equations (to classify the limit profile of the solutions, to wit the elements of the global attractor).
AU  - Efendiyev, M.A.
C1  - 8602
C2  - 30200
SP  - 239-258
TI  - Asymptotics of solutions of semilinear elliptic partial differential equations.
JO  - Adv. Math. Sci. Appl.
VL  - 22
IS  - 1
PB  - Gakkotosho
PY  - 2012
SN  - 1343-4373
ER  - 

TY  - JOUR
AB  - In this article we deal with a class of degenerate parabolic systems that encompasses two different effects: porous medium and chemotaxis. Such classes of equations arise in the mesoscale level modeling of biomass spreading mechanisms via chemotaxis. We prove well-posedness under certain ”balance conditions” on the order of the porous medium degeneracy and the growth of the chemotactic functions.
AU  - Efendiyev, M.A.
AU  - Zhigun, A.
C1  - 6707
C2  - 29144
CY  - Tokyo
SP  - 285-304
TI  - On a 'balance' condition for a class of PDEs including porous medium and chemotaxis effect: Non-aoutonomous case.
JO  - Adv. Math. Sci. Appl.
VL  - 21
IS  - 1
PB  - Gakkotosho
PY  - 2011
SN  - 1343-4373
ER  - 

TY  - JOUR
AB  - We consider a reaction diffusion equation with density dependent diffusion rate. This diffusion rate has a zero of order a> 1 at zero and a singularity of order b> 0 at a threshold density. The reaction term has a zero of order α at the same threshold density. We show that for α − b> −1 there are running fronts, and that there are no running fronts for α − b ≤ 1.
AU  - Efendiyev, M.A.
AU  - Müller, J.*
C1  - 429
C2  - 26981
CY  - Tokyo
SP  - 285-293
TI  - Classification of existence and non-existence of running fronts in case of fast diffusion.
JO  - Adv. Math. Sci. Appl.
VL  - 19
IS  - 1
PB  - Gakkotosho
PY  - 2009
SN  - 1343-4373
ER  - 

TY  - JOUR
AB  - Most bacteria live in biofilm communities, which offer protection against harmful external impacts. This makes treatment of biofilm borne bacterial infections with antibiotics difficult. We discuss a dynamic mathematical model that focuses on the diffusive resistance that a growing biofilm exerts against penetration of antibiotics. This allows bacteria in the protected inner layers to grow while those in the outer rim are inactivated. The model consists of four parabolic partial differential equations for the dependent variables antibiotic concentration, oxygen concentration, active biomass fraction and inert biomass fraction. The equations for the last two variables show power law degeneracy (like the porous medium equation) as the dependent variable vanishes, and a power law singularity (like the fast diffusion equation) as the dependent variable approaches ist a priori known maximum value, and thus are highly non-linear. We show the existence of solutions to this model. This proof uses a positivity criterion, which is formulated and proved as a Lemma for more general nonlinear parabolic systems. Furthermore, a number of computer simulations are carried out to illustrate the behavior of the antibiotic isinfection model in dependence of the antibiotics added to the system.
AU  - Demaret, L.
AU  - Eberl, H.*
AU  - Efendiyev, M.A.
AU  - Lasser, R.
C1  - 927
C2  - 26393
CY  - Tokyo
SP  - 269-304
TI  - Analysis and simulation of a meso-scale model of diffusive restistance of bacterial biofilms to penetration of antibiotics.
JO  - Adv. Math. Sci. Appl.
VL  - 18
IS  - 1
PB  - Gakkotosho
PY  - 2008
SN  - 1343-4373
ER  - 

TY  - JOUR
AU  - Efendiyev, M.A.
AU  - Demaret, L.*
C1  - 5562
C2  - 28306
CY  - Tokyo
SP  - 105-118
TI  - On the structure of attractors for a class of degenerate reaction-diffusion systems.
JO  - Adv. Math. Sci. Appl.
VL  - 18
IS  - 1
PB  - Gakkotosho
PY  - 2008
SN  - 1343-4373
ER  -