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Mathematical Biosciences and Engineering: MBE

Xueyan Yang, Xiaodi Li, Qiang Xi, Peiyong Duan
This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications. After reviewing the relative literatures, this paper provides a comprehensive and intuitive overview of IDSs. Five aspects of IDSs are surveyed including basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses. Then the research prospect is given, which provides a reference for further study of IDSs theory...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Abdelrazig K Tarboush, Jing Ge, Zhigui Lin
This paper is concerned with a strongly-coupled elliptic system, which describes a West Nile virus (WNv) model with cross-diffusion in a heterogeneous environment. The basic reproduction number is introduced through the next generation infection operator and some related eigenvalue problems. The existence of coexistence states is presented by using a method of upper and lower solutions. The true positive solutions are obtained by monotone iterative schemes. Our results show that a cross-diffusive WNv model possesses at least one coexistence solution if the basic reproduction number is greater than one and the cross-diffusion rates are small enough, while if the basic reproduction number is less than or equal to one, the model has no positive solution...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Meng Zhang, Kaiyuan Liu, Lansun Chen, Zeyu Li
A state feedback impulsive model is set up to discuss the spreading and control of the computer worm and virus. Considering the transmission features, saturated infectious is adopted to describe the spreading in the model, and all the treatment measures, such as patching operating system and updating antivirus software, are assumed to take effect instantly. Then the model is analyzed with a novel method, and the existence and stability of order-1 limit cycle are discussed. Finally, the numerical simulation is listed to verify the result of the paper...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Joseph Malinzi, Rachid Ouifki, Amina Eladdadi, Delfim F M Torres, Jane K A White
Oncolytic virotherapy has been emerging as a promising novel cancer treatment which may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how virotherapy could enhance chemotherapy, we propose an ODE based mathematical model describing the interactions between tumour cells, the immune response, and a treatment combination with chemotherapy and oncolytic viruses. Stability analysis of the model with constant chemotherapy treatment rates shows that without any form of treatment, a tumour would grow to its maximum size...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Jianquan Li, Xiaoqin Wang, Xiaolin Lin
The epidemic characteristics of an epidemic model with behavioral change in [V. Capasso, G. Serio, A generalizaition of the Kermack-McKendrick deterministic epidemic model, Math. Bios., 42 (1978), 43-61] are investigated, including the epidemic size, peak and turning point. The conditions on the appearance of the peak state and turning point are represented clearly, and the expressions determining the corresponding time for the peak state and turning point are described explicitly. Moreover, the impact of behavioral change on the characteristics is discussed...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Feng Rao, Carlos Castillo-Chavez, Yun Kang
This paper investigates the complex dynamics of a Harrison-type predator-prey model that incorporating: (1) A constant time delay in the functional response term of the predator growth equation; and (2) environmental noise in both prey and predator equations. We provide the rigorous results of our model including the dynamical behaviors of a positive solution and Hopf bifurcation. We also perform numerical simulations on the effects of delay or/and noise when the corresponding ODE model has an interior solution...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Mondal Hasan Zahid, Christopher M Kribs
Infectious disease outbreaks sometimes overwhelm healthcare facilities. A recent case occurred in West Africa in 2014 when an Ebola virus outbreak overwhelmed facilities in Sierra Leone, Guinea and Liberia. In such scenarios, how many patients can hospitals admit to minimize disease burden? This study considers what type of hospital admission policy during a hypothetical Ebola outbreak can better serve the community, if overcrowding degrades the hospital setting. Our result shows that which policy minimizes loss to the community depends on the initial estimation of the control reproduction number, R₀...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Tianyuan Xu, Shanming Ji, Chunhua Jin, Ming Mei, Jingxue Yin
In this paper, we derive a chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the existing studies focusing on the case of non-degenerate diffusion, this model with degenerate diffusion causes us some essential difficulty on the boundedness estimates and the propagation behavior of its compact support. In the presence of logistic damping, for the early stage before tumour cells spread to the whole domain, we first estimate the expanding speed of tumour region as O(t^β) for 0 < β < 1/2 ...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Arvind Kumar Misra, Rajanish Kumar Rai, Yasuhiro Takeuchi
Public health information through media plays an important role to curb the spread of various infectious diseases as most of the populations rely on what media projects to them. Social media and TV advertisements are important mediums to communicate people regarding the spread of any infectious disease and methods to prevent its spread. Therefore, in this paper, we propose a mathematical model to see how TV and social media advertisements impact the dynamics of an infectious disease. The susceptible population is assumed vulnerable to infection as well as information (through TV and social media ads)...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Suxia Zhang, Hongbin Guo, Robert Smith
Hepatitis B virus (HBV) is responsible for an estimated 378 million infections worldwide and 620, 000 deaths annually. Safe and effective vaccination programs have been available for decades, but coverage is limited due to economic and social factors. We investigate the effect of immigration and infection age on HBV transmission dynamics, incorporating age-dependent immigration flow and vertical transmission. The mathematical model can be used to describe HBV transmission in highly endemic regions with vertical transmission and migration of infected HBV individuals...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Sebastien Motsch, Mehdi Moussaïd, Elsa G Guillot, Mathieu Moreau, Julien Pettré, Guy Theraulaz, Cécile Appert-Rolland, Pierre Degond
Understanding and predicting the collective behaviour of crowds is essential to improve the efficiency of pedestrian flows in urban areas and minimize the risks of accidents at mass events. We advocate for the development of crowd traffic management systems, whereby observations of crowds can be coupled to fast and reliable models to produce rapid predictions of the crowd movement and eventually help crowd managers choose between tailored optimization strategies. Here, we propose a Bi-directional Macroscopic (BM) model as the core of such a system...
December 1, 2018: Mathematical Biosciences and Engineering: MBE
Qi Wang, Lifang Huang, Kunwen Wen, Jianshe Yu
Life growth and development are driven by continuous cell divisions. Cell division is a stochastic and complex process. In this paper, we study the impact of cell division on the mean and noise of mRNA numbers by using a two-state stochastic model of transcription. Our results show that the steady-state mRNA noise with symmetric cell division is less than that with binomial inheritance with probability 0.5, but the steady-state mean transcript level with symmetric division is always equal to that with binomial inheritance with probability 0...
October 1, 2018: Mathematical Biosciences and Engineering: MBE
Alexander P Krishchenko, Konstantin E Starkov
In this paper we examine ultimate dynamics of the four-dimensional model describing interactions between tumor cells, effector immune cells, interleukin -2 and transforming growth factor-beta. This model was elaborated by Arciero et al. and is obtained from the Kirschner-Panetta type model by introducing two various treatments. We provide ultimate upper bounds for all variables of this model and two lower bounds and, besides, study when dynamics of this model possesses a global attracting set. The nonexistence conditions of compact invariant sets are derived...
October 1, 2018: Mathematical Biosciences and Engineering: MBE
Carole Guillevin, Rémy Guillevin, Alain Miranville, Angélique Perrillat-Mercerot
The aim of this article is to study the well-posedness and properties of a fast-slow system which is related with brain lactate kinetics. In particular, we prove the existence and uniqueness of nonnegative solutions and obtain linear stability results. We also give numerical simulations with different values of the small parameter ε and compare them with experimental data.
October 1, 2018: Mathematical Biosciences and Engineering: MBE
József Z Farkas, Gary T Smith, Glenn F Webb
We quantify a recent five-category CT histogram based classification of ground glass opacities using a dynamic mathematical model for the spatial-temporal evolution of malignant nodules. Our mathematical model takes the form of a spatially structured partial differential equation with a logistic crowding term. We present the results of extensive simulations and validate our model using patient data obtained from clinical CT images from patients with benign and malignant lesions.
October 1, 2018: Mathematical Biosciences and Engineering: MBE
Liming Cai, Shangbing Ai, Guihong Fan
To prevent the transmissions of mosquito-borne diseases (e.g., malaria, dengue fever), recent works have considered the problem of using the sterile insect technique to reduce or eradicate the wild mosquito population. It is important to consider how reproductive advantage of the wild mosquito population offsets the success of population replacement. In this work, we explore the interactive dynamics of the wild and sterile mosquitoes by incorporating the delay in terms of the growth stage of the wild mosquitoes...
October 1, 2018: Mathematical Biosciences and Engineering: MBE
Narges Montazeri Shahtori, Tanvir Ferdousi, Caterina Scoglio, Faryad Darabi Sahneh
Recent experience of the Ebola outbreak in 2014 highlighted the importance of immediate response measure to impede transmission in the early stage. To this aim, efficient and effective allocation of limited resources is crucial. Among the standard interventions is the practice of following up with the recent physical contacts of the infected individuals -- known as contact tracing. In an effort to understand the effects of contact tracing protocols objectively, we explicitly develop a model of Ebola transmission incorporating contact tracing...
October 1, 2018: Mathematical Biosciences and Engineering: MBE
Shannon Dixon, Nancy Huntly, Priscilla E Greenwood, Luis F Gordillo
Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming part of these regions into deserts in some cases. Although it is documented that a decreasing tendency in precipitation might induce earlier disappearance of vegetation, quantifying the relationship between decrease of precipitation and vegetation endurance remains a challenging task due to the inherent complexities involved in distinct scenarios...
October 1, 2018: Mathematical Biosciences and Engineering: MBE
Laurenz Göllmann, Helmut Maurer
There exists an extensive literature on delay differential models in biology and biomedicine, but only a few papers study such models in the framework of optimal control theory. In this paper, we consider optimal control problems with multiple time delays in state and control variables and present two applications in biomedicine. After discussing the necessary optimality conditions for delayed optimal control problems with control-state constraints, we propose discretization methods by which the delayed optimal control problem is transformed into a large-scale nonlinear programming problem...
October 1, 2018: Mathematical Biosciences and Engineering: MBE
Adam Peddle, William Lee, Tuoi Vo
The aim of a drug eluting stent is to prevent restenosis of arteries following percutaneous balloon angioplasty. A long term goal of research in this area is to use modelling to optimise the design of these stents to maximise their efficiency. A key obstacle to implementing this is the lack of a mathematical model of the biology of restenosis. Here we investigate whether mathematical models of cancer biology can be adapted to model the biology of restenosis and the effect of drug elution. We show that relatively simple, rate kinetic models give a good description of available data of restenosis in animal experiments, and its modification by drug elution...
October 1, 2018: Mathematical Biosciences and Engineering: MBE
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