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Journal of Biological Dynamics

Hai-Feng Huo, Shui-Rong Huang, Xun-Yang Wang, Hong Xiang
A new social epidemic model to depict alcoholism with media coverage is proposed in this paper. Some fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated. Stability of all equilibria are studied. The existence of the optimal control pair and mathematical expressions of optimal control are obtained by Pontryagin's maximum principle. Numerical simulations are also performed to illustrate our results. Our results show that media coverage is an effective measure to quit drinking...
May 11, 2017: Journal of Biological Dynamics
Thomas Hillen, Diana White, Gerda de Vries, Adriana Dawes
Microtubules (MTs) are protein filaments that provide structure to the cytoskeleton of cells and a platform for the movement of intracellular substances. The spatial organization of MTs is crucial for a cell's form and function. MTs interact with a class of proteins called motor proteins that can transport and position individual filaments, thus contributing to overall organization. In this paper, we study the mathematical properties of a coupled partial differential equation (PDE) model, introduced by White et al...
April 20, 2017: Journal of Biological Dynamics
Qasim Ali, Lindi M Wahl
Clustered regularly interspaced short palindromic repeats (CRISPR), linked with CRISPR associated (Cas) genes, can confer adaptive immunity to bacteria, against bacteriophage infections. Thus from a therapeutic standpoint, CRISPR immunity increases biofilm resistance to phage therapy. Recently, however, CRISPR-Cas genes have been implicated in reducing biofilm formation in lysogenized cells. Thus CRISPR immunity can have complex effects on phage-host-lysogen interactions, particularly in a biofilm. In this contribution, we develop and analyse a series of dynamical systems to elucidate and disentangle these interactions...
April 20, 2017: Journal of Biological Dynamics
Yuanwei Qi, Yi Zhu
This article studies existence and stability of travelling wave of unstirred Gray-Scott system in biological pattern formation which models an isothermal chemical reaction [Formula: see text] involving two chemical species, a reactant A and an auto-catalyst B, and a linear decay [Formula: see text], where C is an inert product. Our result shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different travelling pulses than related models in the literature...
April 10, 2017: Journal of Biological Dynamics
Hai-Feng Huo, Yong-Lan Chen, Hong Xiang
A more realistic binge drinking model with time delay is introduced. Time delay is used to represent the time lag of the immunity against drinking in our model. For the model without the time delay, using Routh-Hurwitz criterion, we obtain that the alcohol-free equilibrium is locally asymptotically stable if [Formula: see text]. We also obtain that the unique alcohol-present equilibrium is locally asymptotically stable if [Formula: see text]. For the model with time delay, the local stability of all the equilibria is derived...
December 2017: Journal of Biological Dynamics
Alfred Hugo, Oluwole Daniel Makinde, Santosh Kumar, Fred F Chibwana
In this paper, a deterministic compartmental eco- epidemiological model with optimal control of Newcastle disease (ND) in Tanzania is proposed and analysed. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin's maximum principle and the numerical values of model parameters were estimated using maximum likelihood estimator. Three control strategies were incorporated such as chicken vaccination (preventive), human education campaign and treatment of infected human (curative) and its' impact were graphically observed...
December 2017: Journal of Biological Dynamics
Abdul Qadeer Khan, Jiying Ma, Dongmei Xiao
In this paper, we study the global dynamics and bifurcations of a two-dimensional discrete time host-parasitoid model with strong Allee effect. The existence of fixed points and their stability are analysed in all allowed parametric region. The bifurcation analysis shows that the model can undergo fold bifurcation and Neimark-Sacker bifurcation. As the parameters vary in a small neighbourhood of the Neimark-Sacker bifurcation condition, the unique positive fixed point changes its stability and an invariant closed circle bifurcates from the positive fixed point...
December 2017: Journal of Biological Dynamics
Mingzhan Huang, Xinyu Song, Jia Li
To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback...
December 2017: Journal of Biological Dynamics
Tahir Khan, Gul Zaman, M Ikhlaq Chohan
In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number [Formula: see text]. We show that if [Formula: see text] then the disease-free equilibrium is both locally as well as globally asymptotically stable. Then, we prove that the model is locally and globally asymptotically stable, if [Formula: see text]...
December 2017: Journal of Biological Dynamics
Christian Cuba Samaniego, Giulia Giordano, Franco Blanchini, Elisa Franco
Oscillators are essential to fuel autonomous behaviours in molecular systems. Artificial oscillators built with programmable biological molecules such as DNA and RNA are generally easy to build and tune, and can serve as timers for biological computation and regulation. We describe a new artificial nucleic acid biochemical reaction network, and we demonstrate its capacity to exhibit oscillatory solutions. This network can be built in vitro using nucleic acids and three bacteriophage enzymes, and has the potential to be implemented in cells...
December 2017: Journal of Biological Dynamics
Vitalii Akimenko, Roumen Anguelov
In this paper we study the nonlinear age-structured model of a polycyclic two-phase population dynamics including delayed effect of population density growth on the mortality. Both phases are modelled as a system of initial boundary values problem for semi-linear transport equation with delay and initial problem for nonlinear delay ODE. The obtained system is studied both theoretically and numerically. Three different regimes of population dynamics for asymptotically stable states of autonomous systems are obtained in numerical experiments for the different initial values of population density...
December 2017: Journal of Biological Dynamics
Aitziber Ibañez
The Lotka-Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting both species as the control variable. We analyse the optimal hunting problem paying special attention to the nature of the optimal state and control trajectories in long time intervals. To do that, we apply recent theoretical results on the frame to show that, when the time horizon is large enough, optimal strategies are nearly steady-state...
December 2017: Journal of Biological Dynamics
Alina Constantinescu
The aim of our study is to improve the crop planning procedures using neuro-fuzzy concepts. In this paper we design a neuro-fuzzy procedure that offers the suitable maize hybrid, from a set of preferred hybrids, which must be organically farmed in the current year. Our method is a statistical one, on the one hand it processes data provided by the previous years and on the other hand it takes in account the vague character of the environmental factors. Also we present here some experimental results obtained by us on a certain set of real data, results which prove the efficiency of our approach...
December 2017: Journal of Biological Dynamics
Huitao Zhao, Miaochan Zhao
An susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity...
December 2017: Journal of Biological Dynamics
Xueying Wang, Jin Wang
Novel deterministic and stochastic models are proposed in this paper for the within-host dynamics of cholera, with a focus on the bacterial-viral interaction. The deterministic model is a system of differential equations describing the interaction among the two types of vibrios and the viruses. The stochastic model is a system of Markov jump processes that is derived based on the dynamics of the deterministic model. The multitype branching process approximation is applied to estimate the extinction probability of bacteria and viruses within a human host during the early stage of the bacterial-viral infection...
December 22, 2016: Journal of Biological Dynamics
Yan-Xia Dang, Xue-Zhi Li, Maia Martcheva
In this paper, a multi-strain model that links immunological and epidemiological dynamics across scales is formulated. On the within-host scale, the n strains eliminate each other with the strain having the largest immunological reproduction number persisting. However, on the population scale, we extend the competitive exclusion principle to a multi-strain model of SI-type for the dynamics of highly pathogenic flu in poultry that incorporates both the infection age of infectious individuals and biological age of pathogen in the environment...
December 2016: Journal of Biological Dynamics
N G Cadigan, S Wang
We study the sensitivity of fishery management per-recruit harvest rates which may be part of a quantitative harvest strategy designed to achieve some objective for catch or population size. We use a local influence sensitivity analysis to derive equations that describe how these reference harvest rates are affected by perturbations to productivity processes. These equations give a basic theoretical understanding of sensitivity that can be used to predict what the likely impacts of future changes in productivity will be...
December 2016: Journal of Biological Dynamics
Aziz Ullah Awan, Muhammad Ozair, Qamar Din, Takasar Hussain
This work is related to qualitative behaviour of an epidemic model of pine wilt disease. More precisely, we proved that the reproductive number has sharp threshold properties. It has been shown that how vector population can be reduced by the periodic use of insecticides. Numerical simulations show that epidemic level of infected vectors becomes independent of saturation level by including the transmission through mating.
December 2016: Journal of Biological Dynamics
Christian T K-H Stadtländer
No abstract text is available yet for this article.
December 2016: Journal of Biological Dynamics
Fang Yu, Lin Wang, James Watmough
In many existing predator-prey or plant-herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant-herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations...
December 2016: Journal of Biological Dynamics
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