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Journal of Biological Dynamics

Xia Wang, Sanyi Tang, Xinyu Song, Libin Rong
HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states...
October 12, 2016: Journal of Biological Dynamics
Alex Petric, Ernesto Guzman-Novoa, Hermann J Eberl
We present a mathematical model (a) for the infection of a honey bee colony with Nosema ceranae. This is a system of five ordinary differential equations for the dependent variables healthy and infected worker bees in the hive, healthy and infected forager bees, and disease potential deposited in the hive. The model is then (b) extended to account for increased forager losses, e.g. caused by exposure to external stressors. The model is non-autonomous with periodic coefficient functions. Algebraic complexity prevents a rigorous mathematical analysis...
October 5, 2016: Journal of Biological Dynamics
Min Yu, Yueping Dong, Yasuhiro Takeuchi
In this paper, a previous tumour-immune interaction model is simplified by neglecting a relatively weak direct immune activation by the tumour cells, which can still keep the essential dynamics properties of the original model. As the immune activation process is not instantaneous, we now incorporate one delay for the activation of the effector cells (ECs) by helper T cells (HTCs) into the model. Furthermore, we investigate the stability and instability regions of the tumour-presence equilibrium state of the delay-induced system with respect to two parameters, the activation rate of ECs by HTCs and the HTCs stimulation rate by the presence of identified tumour antigens...
September 20, 2016: Journal of Biological Dynamics
Xueying Wang, Jin Wang
A new modelling framework is proposed to study the within-host and between-host dynamics of cholera, a severe intestinal infection caused by the bacterium Vibrio cholerae. The within-host dynamics are characterized by the growth of highly infectious vibrios inside the human body. These vibrios shed from humans contribute to the environmental bacterial growth and the transmission of the disease among humans, providing a link from the within-host dynamics at the individual level to the between-host dynamics at the population and environmental level...
September 19, 2016: Journal of Biological Dynamics
Ling Xue, Carrie A Manore, Panpim Thongsripong, James M Hyman
We develop and analyse an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachia-infected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit some viral mosquito-transmitted diseases, including dengue fever, chikungunya, and Zika. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to establish an endemic infection in a wild mosquito population...
September 14, 2016: Journal of Biological Dynamics
Jinliang Wang, Jiying Lang, Yuming Chen
A susceptible-vaccinated-infectious-recovered epidemic model with infection age and relapse age has been formulated. We first address the asymptotic smoothness of the solution semiflow, existence of a global attractor, and uniform persistence of the model. Then by constructing suitable Volterra-type Lyapunov functionals, we establish a global threshold dynamics of the model, which is determined by the basic reproduction number. Biologically, it is confirmed that neglecting the possibility of vaccinees getting infected will over-estimate the effect of vaccination strategies...
September 3, 2016: Journal of Biological Dynamics
Jia Li
Based on previous research, we formulate revised, new, simple models for interactive wild and sterile mosquitoes which are better approximations to real biological situations but mathematically more tractable. We give basic investigations of the dynamical features of these simple models such as the existence of equilibria and their stability. Numerical examples to demonstrate our findings and brief discussions are also provided.
August 10, 2016: 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
(no author information available yet)
No abstract text is available yet for this article.
December 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
V M Veliov, A Widder
UNLABELLED: The paper presents a model for the evolution of an infectious disease in a population with individual-specific immunity. The immune state of an individual varies with time according to its own dynamics, depending on whether the individual is infected or not. The model involves a system of size-structured (first-order) PDEs that capture both the dynamics of the immune states and the transition between compartments consisting of infected, susceptible, etc. INDIVIDUALS: Due to the unavailability of precise data about the immune states of the individuals, the main focus in the paper is on developing a technique for set-membership estimations of aggregated quantities of interest...
December 2016: Journal of Biological Dynamics
Fan Bai
One crucial condition for the uniqueness of Nash equilibrium set in vaccination games is that the attack ratio monotonically decreases as the vaccine coverage level increasing. We consider several deterministic vaccination models in homogeneous mixing population and in heterogeneous mixing population. Based on the final size relations obtained from the deterministic epidemic models, we prove that the attack ratios can be expressed in terms of the vaccine coverage levels, and also prove that the attack ratios are decreasing functions of vaccine coverage levels...
December 2016: Journal of Biological Dynamics
Fred Brauer
We consider an epidemic model in which all disease transmission is through shedding of virus by infectives and acquisition by susceptibles, rather than by direct contact. This leads to an susceptible-infectious-virus-removed (SIVR) model for which we can determine the basic reproduction number and the final size relation. We extend the model to an age of infection model with virus shedding a function of the age of infection.
July 19, 2016: Journal of Biological Dynamics
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