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Mathematical Biosciences and Engineering: MBE

Linhua Zhou, Meng Fan, Qiang Hou, Zhen Jin, Xiangdong Sun
A multigroup model is developed to characterize brucellosis transmission, to explore potential effects of key factors, and to prioritize control measures. The global threshold dynamics are completely characterized by theory of asymptotic autonomous systems and Lyapunov direct method. We then formulate a multi-objective optimization problem and, by the weighted sum method, transform it into a scalar optimization problem on minimizing the total cost for control. The existence of optimal control and its characterization are well established by Pontryagin's Maximum Principle...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Bo Zheng, Wenliang Guo, Linchao Hu, Mugen Huang, Jianshe Yu
Dengue, malaria, and Zika are dangerous diseases primarily transmitted by Aedes aegypti, Aedes albopictus, and Anopheles stephensi. In the last few years, a new disease control method, besides pesticide spraying to kill mosquitoes, has been developed by releasing mosquitoes carrying bacterium Wolbachia into the natural areas to infect the wild population of mosquitoes and block disease transmission. The bacterium is transmitted by infected mothers and the maternal transmission was assumed to be perfect in virtually all previous models...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Wenjun Xia, Jinzhi Lei
Translation is a central biological process by which proteins are synthesized from genetic information contained within mRNAs. Here, we investigate the kinetics of translation at the molecular level by a stochastic simulation model. The model explicitly includes RNA sequences, ribosome dynamics, the tRNA pool and biochemical reactions involved in the translation elongation. The results show that the translation efficiency is mainly limited by the available ribosome number, translation initiation and the translation elongation time...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Markus Thäter, Kurt Chudej, Hans Josef Pesch
In this paper an improved SEIR model for an infectious disease is presented which includes logistic growth for the total population. The aim is to develop optimal vaccination strategies against the spread of a generic disease. These vaccination strategies arise from the study of optimal control problems with various kinds of constraints including mixed control-state and state constraints. After presenting the new model and implementing the optimal control problems by means of a first-discretize-then-optimize method, numerical results for six scenarios are discussed and compared to an analytical optimal control law based on Pontrygin's minimum principle that allows to verify these results as approximations of candidate optimal solutions...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Notice Ringa, Chris T Bauch
Pair approximation models have been used to study the spread of infectious diseases in spatially distributed host populations, and to explore disease control strategies such as vaccination and case isolation. Here we introduce a pair approximation model of individual uptake of non-pharmaceutical interventions (NPIs) for an acute self-limiting infection, where susceptible individuals can learn the NPIs either from other susceptible individuals who are already practicing NPIs ("social learning"), or their uptake of NPIs can be stimulated by being neighbours of an infectious person ("exposure learning")...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Arti Mishra, Benjamin Ambrosio, Sunita Gakkhar, M A Aziz-Alaoui
In this paper, a network model has been proposed to control dengue disease transmission considering host-vector dynamics in n patches. The control of mosquitoes is performed by SIT. In SIT, the male insects are sterilized in the laboratory and released into the environment to control the number of offsprings. The basic reproduction number has been computed. The existence and stability of various states have been discussed. The bifurcation diagram has been plotted to show the existence and stability regions of disease-free and endemic states for an isolated patch...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Bashar Ibrahim
The precise regulation of cell life division is indispensable to the reliable inheritance of genetic material, i.e. DNA, in successive generations of cells. This is governed by dedicated biochemical networks which ensure that all requirements are met before transition from one phase to the next. The Spindle Assembly Checkpoint (SAC) is an evolutionarily mechanism that delays mitotic progression until all chromosomes are properly linked to the mitotic spindle. During some asymmetric cell divisions, such as those observed in budding yeast, an additional mechanism, the Spindle Position Checkpoint (SPOC), is required to delay exit from mitosis until the mitotic spindle is correctly aligned...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Eduardo Ibarguen-Mondragon, Lourdes Esteva, Edith Mariela Burbano-Rosero
In this work we formulate a model for the population dynamics of Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB). Our main interest is to assess the impact of the competition among bacteria on the infection prevalence. For this end, we assume that Mtb population has two types of growth. The first one is due to bacteria produced in the interior of each infected macrophage, and it is assumed that is proportional to the number of infected macrophages. The second one is of logistic type due to the competition among free bacteria released by the same infected macrophages...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Mayee Chen, Junping Shi
It is a common understanding that rotational cattle grazing provides better yields than continuous grazing, but a quantitative analysis is lacking in agricultural literature. In rotational grazing, cattle periodically move among paddocks in contrast to continuous grazing, in which the cattle graze on a single plot for the entire grazing season. We construct a differential equation model of vegetation grazing on a fixed area to show that production yields and stockpiled forage are greater for rotational grazing than continuous grazing...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Zhan Chen, Yuting Zou
In this paper, a novel multiscale method is proposed for the study of heterogeneous tumor spheroid growth in vitro. The entire tumor spheroid is described by an ellipsoid-based model while nutrient and other environmental factors are treated as continua. The ellipsoid-based discrete component is capable of incorporating mechanical effects and deformability, while keeping a minimum set of free variables to describe complex shape variations. Moreover, our purely cell-based description of tumor avoids the complex mutual conversion between a cell-based model and continuum model within a tumor, such as force and mass transformation...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Erin N Bodine, Connor Cook, Mikayla Shorten
The 2014 outbreak of Ebola virus disease (EVD) in West Africa was multinational and of an unprecedented scale primarily affecting the countries of Guinea, Liberia, and Sierra Leone. One of the qualities that makes EVD of high public concern is its potential for extremely high mortality rates (up to 90%). A prophylactic vaccine for ebolavirus (rVSV-ZEBOV) has been developed, and clinical trials show near-perfect efficacy. We have developed an ordinary differential equations model that simulates an EVD epidemic and takes into account (1) transmission through contact with infectious EVD individuals and deceased EVD bodies, (2) the heterogeneity of the risk of becoming infected with EVD, and (3) the increased survival rate of infected EVD patients due to greater access to trained healthcare providers...
April 1, 2018: Mathematical Biosciences and Engineering: MBE
Zuzana Chladná
The recent measles outbreaks in US and Germany emphasize the importance of sustaining and increasing vaccination rates. In Slovakia, despite mandatory vaccination scheme, decrease in the vaccination rates against measles has been observed in recent years. Different kinds of intervention at the state level, like a law making vaccination a requirement for school entry or education and advertising seem to be the only strategies to improve vaccination coverage. This study aims to analyze the economic effectiveness of intervention in Slovakia...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
Bruno Buonomo, Giuseppe Carbone, Alberto d'Onofrio
We extend here the game-theoretic investigation made by d'Onofrio et al (2012) on the interplay between private vaccination choices and actions of the public health system (PHS) to favor vaccine propensity in SIR-type diseases. We focus here on three important features. First, we consider a SEIR--type disease. Second, we focus on the role of seasonal fluctuations of the transmission rate. Third, by a simple population--biology approach we derive - with a didactic aim - the game theoretic equation ruling the dynamics of vaccine propensity, without employing 'economy--related' concepts such as the payoff...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
Ping Yan
For an intervention against the spread of communicable diseases, the idealized situation is when individuals fully comply with the intervention and the exposure to the infectious agent is comparable across all individuals. Some level of non-compliance is likely where the intervention is widely implemented. The focus is on a more accurate view of its effects population-wide. A frailty model is applied. Qualitative analysis, in mathematical terms, reveals how large variability in compliance renders the intervention less effective...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
Semu Mitiku Kassa
Funds from various global organizations, such as, The Global Fund, The World Bank, etc. are not directly distributed to the targeted risk groups. Especially in the so-called third-world-countries, the major part of the fund in HIV prevention programs comes from these global funding organizations. The allocations of these funds usually pass through several levels of decision making bodies that have their own specific parameters to control and specific objectives to achieve. However, these decisions are made mostly in a heuristic manner and this may lead to a non-optimal allocation of the scarce resources...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
Surabhi Pandey, Ezio Venturino
Tuberculosis (TB) is returning to be a worldwide global public health threat. It is estimated that 9.6 million cases occurred in 2014, of which just two-thirds notified to public health authorities. The "missing cases" constitute a severe challenge for TB transmission control. TB is a severe disease in India, while, worldwide, the WHO estimates that one third of the entire world population is infected. Nowadays, incidence estimation relies increasingly more on notifications of new cases from routine surveillance...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
Vasiliy N Leonenko, Sergey V Ivanov
This paper is dedicated to the application of two types of SEIR models to the influenza outbreak peak prediction in Russian cities. The first one is a continuous SEIR model described by a system of ordinary differential equations. The second one is a discrete model formulated as a set of difference equations, which was used in the Baroyan-Rvachev modeling framework for the influenza outbreak prediction in the Soviet Union. The outbreak peak day and height predictions were performed by calibrating both models to varied-size samples of long-term data on ARI incidence in Moscow, Saint Petersburg, and Novosibirsk...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
Federico Papa, Francesca Binda, Giovanni Felici, Marco Franzetti, Alberto Gandolfi, Carmela Sinisgalli, Claudia Balotta
In the present paper we propose a simple time-varying ODE model to describe the evolution of HIV epidemic in Italy. The model considers a single population of susceptibles, without distinction of high-risk groups within the general population, and accounts for the presence of immigration and emigration, modelling their effects on both the general demography and the dynamics of the infected subpopulations. To represent the intra-host disease progression, the untreated infected population is distributed over four compartments in cascade according to the CD4 counts...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
David J Gerberry
When mathematical models of infectious diseases are used to inform health policy, an important first step is often to calibrate a model to disease surveillance data for a specific setting (or multiple settings). It is increasingly common to also perform sensitivity analyses to demonstrate the robustness, or lack thereof, of the modeling results. Doing so requires the modeler to find multiple parameter sets for which the model produces behavior that is consistent with the surveillance data. While frequently overlooked, the calibration process is nontrivial at best and can be inefficient, poorly communicated and a major hurdle to the overall reproducibility of modeling results...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
Andreas Widder
We present a method, known in control theory, to give set-membership estimates for the states of a population in which an infectious disease is spreading. An estimation is reasonable due to the fact that the parameters of the equations describing the dynamics of the disease are not known with certainty. We discuss the properties of the resulting estimations. These include the possibility to determine best- or worst-case-scenarios and identify under which circumstances they occur, as well as a method to calculate confidence intervals for disease trajectories under sparse data...
February 1, 2018: Mathematical Biosciences and Engineering: MBE
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