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Journal of Biological Dynamics

Jingan Cui, Yanan Zhang, Zhilan Feng
In meta-population models for infectious diseases, the basic reproduction number [Formula: see text] can be as much as 70% larger in the case of preferential mixing than that in homogeneous mixing [J.W. Glasser, Z. Feng, S.B. Omer, P.J. Smith, and L.E. Rodewald, The effect of heterogeneity in uptake of the measles, mumps, and rubella vaccine on the potential for outbreaks of measles: A modelling study, Lancet ID 16 (2016), pp. 599-605. doi: 10.1016/S1473-3099(16)00004-9 ]. This suggests that realistic mixing can be an important factor to consider in order for the models to provide a reliable assessment of intervention strategies...
June 18, 2018: Journal of Biological Dynamics
Fred Brauer
Early in a disease outbreak, it is important to be able to estimate the final size of the epidemic in order to assess needs for treatment and to be able to compare the effects of different treatment approaches. However, it is common for epidemics, especially of diseases considered dangerous, to grow much more slowly than expected. We suggest that by assuming behavioural changes in the face of an epidemic and heterogeneity of mixing in the population it is possible to obtain reasonable early estimates.
May 9, 2018: Journal of Biological Dynamics
Melody Walker, Julie C Blackwood, Vicki Brown, Lauren M Childs
Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations...
April 27, 2018: Journal of Biological Dynamics
Zijian Liu, Lei Zhang, Ping Bi, Jianhua Pang, Bing Li, Chengling Fang
In this paper, a one-prey-n-predator impulsive reaction-diffusion periodic predator-prey system with ratio-dependent functional response is investigated. On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditions on the ultimate boundedness and permanence of the predator-prey system are established. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained...
December 2018: Journal of Biological Dynamics
Jin Yang, Yuanshun Tan
We establish a Holling II predator-prey system with pesticide dose response non-linear pulses and then study the global dynamics of the model. First, we construct the Poincaré map in the phase set and discuss its main properties. Second, threshold conditions for the existence and stability of boundary periodic solution and order-[Formula: see text] periodic solutions have been provided. The results show that the pesticide dose increases when the period of control increases, while it will decrease as threshold increases...
December 2018: Journal of Biological Dynamics
Wenjun Jing, Zhen Jin, Juping Zhang
The demography and infection age play an important role in the spread of slowly progressive diseases. To investigate their effects on the disease spreading, we propose a pairwise epidemic model with infection age and demography on dynamic networks. The basic reproduction number of this model is derived. It is proved that there is a disease-free equilibrium which is globally asymptotically stable if the basic reproduction number is less that unity. Besides, sensitivity analysis is performed and shows that increasing the variance in recovery time and decreasing the variance in infection time can effectively control the diseases...
December 2018: Journal of Biological Dynamics
Donald A French, Marisa Eisenberg, Tony Nance, Zeynep Teymuroglu
Two simple models for the spread of heavy drinking among a network of individuals are re-introduced and analysed. We provide theorems on the spread of alcohol abuse for these models in cases involving simple connection schemes. Indicators for this spread that resemble the [Formula: see text] used in disease assessment are suggested and studied. We further provide computations with our models on general application networks and begin to study the reliability of the spread indicators.
December 2018: Journal of Biological Dynamics
Nikolaos Askitas
This paper suggests a new way to think about a famous question: what explains cooperation in nature and in particular in humans? I argue that, for an evolutionary biologist as well as a quantitative social scientist, the triangle of two 'teammates' in the presence of a predator (passing and shooting in two-on-one situations) is one of the fundamental conceptual building-blocks for understanding these phenomena because in such a situation the fact that life is packaged in many distinct enclosures (and not in one big monolithic blob) can unfold its comparative advantage...
December 2018: Journal of Biological Dynamics
Jingjing Xu, Geoff Wild
Metapopulations are collections of local populations connected by dispersal. Metapopulation models often assume would-be colonists affect the states of local populations they disperse from and those they disperse to. Here, we build a new framework to include that effect and to assess the impact of dispersal. Our model predicts that a metapopulation will, in general, be found either in the state of global extinction or in the state of persistence. Our key finding is that dispersal, and the state changes associated with dispersal, have significant qualitative and quantitative effects on long-term dynamics only in a narrow range of parameter space...
December 2018: Journal of Biological Dynamics
Kaihong Zhao
In this paper, we study the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.
December 2018: Journal of Biological Dynamics
Traoré Bakary, Sangaré Boureima, Traoré Sado
In this paper, we present a mathematical model of malaria transmission dynamics with age structure for the vector population and a periodic biting rate of female anopheles mosquitoes. The human population is divided into two major categories: the most vulnerable called non-immune and the least vulnerable called semi-immune. By applying the theory of uniform persistence and the Floquet theory with comparison principle, we analyse the stability of the disease-free equilibrium and the behaviour of the model when the basic reproduction ratio [Formula: see text] is greater than one or less than one...
December 2018: Journal of Biological Dynamics
Jummy Funke David
We develop an age of infection model with heterogeneous mixing in which indirect pathogen transmission is considered as a good way to describe contact that is usually considered as direct and we also incorporate virus shedding as a function of age of infection. The simplest form of SIRP epidemic model is introduced and it serves as a basis for the age of infection model and a 2-patch SIRP model where the risk of infection is solely dependent on the residence times and other environmental factors. The computation of the basic reproduction number [Formula: see text], the initial exponential growth rate and the final size relation is done and by mathematical analysis, we study the impact of patches connection and use the final size relation to analyse the ability of disease to invade over a short period of time...
December 2018: Journal of Biological Dynamics
Xin-You Meng, Ni-Ni Qin, Hai-Feng Huo
In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem...
December 2018: Journal of Biological Dynamics
Joseph Páez Chávez, Dirk Jungmann, Stefan Siegmund
The paper presents a comprehensive numerical study of mathematical models used to describe complex biological systems in the framework of integrated pest management. Our study considers two specific ecosystems that describe the application of control mechanisms based on pesticides and natural enemies, implemented in an impulsive and periodic manner, due to which the considered models belong to the class of impulsive differential equations. The present work proposes a numerical approach to study such type of models in detail, via the application of path-following (continuation) techniques for nonsmooth dynamical systems, via the novel continuation platform COCO (Dankowicz and Schilder)...
December 2018: Journal of Biological Dynamics
Robert Stephen Cantrell, Chris Cosner, Xiao Yu
Most classical models for the movement of organisms assume that all individuals have the same patterns and rates of movement (for example, diffusion with a fixed diffusion coefficient) but there is empirical evidence that movement rates and patterns may vary among different individuals. A simple way to capture variation in dispersal that has been suggested in the ecological literature is to allow individuals to switch between two distinct dispersal modes. We study models for populations whose members can switch between two different nonzero rates of diffusion and whose local population dynamics are subject to density dependence of logistic type...
December 2018: Journal of Biological Dynamics
S Elaydi, E Kwessi, G Livadiotis
A general notion of the Allee effect for higher dimensional triangular maps is proposed. A global dynamics theory is established. The theory is applied to multi-species hierarchical models. Then we provide a detailed study of the global dynamics of three-species Ricker competition models with the Allee effect. Regions of extinction, exclusion and coexistence are identified.
December 2018: Journal of Biological Dynamics
Hidekazu Yoshioka, Yuta Yaegashi
A stochastic control model for finding an ecologically sound, fit-for-purpose dam operation policy to suppress bloom of attached algae in its downstream is presented. A singular exactly solvable and a more realistic regular-singular cases are analysed in terms of a Hamilton-Jacobi-Bellman equation. Regularity and consistency of the value function are analysed and its classical verification theorem is established. Practical implications of the mathematical analysis results are discussed focusing on parameter dependence of the optimal controls...
December 2018: Journal of Biological Dynamics
Hsiu-Chuan Wei
A previously published mathematical model, governing tumour growth with mixed immunotherapy and chemotherapy treatments, is modified and studied. The search time, which is assumed to be neglectable in the previously published model, is incorporated into the functional response for tumour-cell lysis by effector cells. The model exhibits bistability where a tumour-cell population threshold exists. A tumour with an initial cell population below the threshold can be controlled by the immune system and remains microscopic and asymptomatic called cancer without disease while that above the threshold grows to lethal size...
December 2018: Journal of Biological Dynamics
Brian P Yurk, Christina A Cobbold
An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction-diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system...
December 2018: Journal of Biological Dynamics
Rui Xu
In this paper, an epidemiological model with age of infection and disease relapse is investigated. The basic reproduction number for the model is identified, and it is shown to be a sharp threshold to completely determine the global dynamics of the model. By analysing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By means of suitable Lyapunov functionals and LaSalle's invariance principle, it is verified that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable, and hence the disease dies out; if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable and the disease becomes endemic...
December 2018: Journal of Biological Dynamics
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