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Journal of Biological Dynamics

Aadrita Nandi, Linda J S Allen
Stochastic epidemic models with two groups are formulated and applied to emerging and re-emerging infectious diseases. In recent emerging diseases, disease spread has been attributed to superspreaders, highly infectious individuals that infect a large number of susceptible individuals. In some re-emerging infectious diseases, disease spread is attributed to waning immunity in susceptible hosts. We apply a continuous-time Markov chain (CTMC) model to study disease emergence or re-emergence from different groups, where the transmission rates depend on either the infectious host or the susceptible host...
November 1, 2018: Journal of Biological Dynamics
Qasim Ali
Bacteriophage can be an effective means of regulating bacterial populations when conditions allow phage invasion of bacterial colonies. Phage can either infect and lyse a host cell, or insert their DNA into the host cell genome; the latter process is called lysogeny. The clustered regularly interspaced short palindromic repeat (CRISPR) system, linked with CRISPR-associated (Cas) genes, is a regulatory system present in a variety of bacteria which confers immunity against bacteriophage. Studies of the group behaviour of bacteria with CRISPR/Cas systems have provided evidence that CRISPR in lysogenized bacteria can cause an inability to form biofilm...
October 7, 2018: Journal of Biological Dynamics
Peter Chesson
The study of the role of environmental variation in community dynamics has traditionally assumed that the environment is a stationary stochastic process or a periodic deterministic process. However, the physical environment in nature is nonstationary. Moreover, anthropogenically driven climate change provides a new challenge emphasizing a persistent but frequently ignored problem: how to make predictions about the dynamics of communities when the nonstationarity of the physical environment is recognized. Recent work is providing a path to conclusions with none of the traditional assumptions of environmental stationarity or periodicity...
September 30, 2018: Journal of Biological Dynamics
Qimin Huang, Xi Huo, Darlene Miller, Shigui Ruan
A deterministic mathematical model with periodic antibiotic prescribing rate is constructed to study the seasonality of Methicillin-resistant Staphylococcus aureus (MRSA) infections taking antibiotic exposure and environmental contamination into consideration. The basic reproduction number [Formula: see text] for the periodic model is calculated under the assumption that there are only uncolonized patients with antibiotic exposure at admission. Sensitivity analysis of [Formula: see text] with respect to some essential parameters is performed...
August 22, 2018: Journal of Biological Dynamics
Zhong-Kai Guo, Hai-Feng Huo, Hong Xiang
In this paper, we investigate a new alcoholism model in which alcoholics have age structure. We rewrite the model as an abstract non-densely defined Cauchy problem and obtain the condition which guarantees the existence of the unique positive steady state. By linearizing the model at steady state and analyzing the associated characteristic transcendental equations, we study the local asymptotic stability of the steady state. Furthermore, by using Hopf bifurcation theorem in Liu et al. (Z. Angew. Math. Phys...
December 2018: Journal of Biological Dynamics
Ophir Nave, Miriam Elbaz
We propose a new method to solve a system of complex ordinary differential equations (ODEs) with hidden hierarchy. Given a complex system of the ODE, the hierarchy of the system is generally hidden. Once we reveal the hierarchy of the system, the system can be reduced into subsystems called slow and fast subsystems. This division of slow and fast subsystems reduces the analysis and hence reduces the computation time, which can be expensive. In our new method, we first apply the singularly perturbed vector field method that is the global quasi-linearization method...
December 2018: Journal of Biological Dynamics
P van den Driessche, Abdul-Aziz Yakubu
We use a general autonomous discrete-time infectious disease model to extend the next generation matrix approach for calculating the basic reproduction number, [Formula: see text], to account for populations with locally asymptotically stable period k cycles in the disease-free systems, where [Formula: see text]. When [Formula: see text] and the demographic equation (in the absence of the disease) has a locally asymptotically stable period k population cycle, we prove the local asymptotic stability of the disease-free period k cycle...
December 2018: Journal of Biological Dynamics
Yu Yang, Alhaji Cherif, Yuxin Zhang
In this paper, we analyze a mathematical model for an inflammatory response to bacterial infection of homogeneous tissues. Specifically, we provide a detailed analysis of the Lauffenburger-Kennedy bacterial infection model and show that the model exhibits three possible equilibria corresponding to a bacteria-free and two endemic compromised steady states. Asymptotic results of the steady states along with the existences of saddle-node connection Hopf bifurcations are shown under certain conditions of the parameters...
December 2018: Journal of Biological Dynamics
Necibe Tuncer, Chindu Mohanakumar, Samuel Swanson, Maia Martcheva
The largest outbreak of Ebola to date is the 2014 West Africa Ebola outbreak, with more than 10,000 cases and over 4000 deaths reported in Liberia alone. To control the spread of the outbreak, multiple interventions were implemented: identification and isolation of cases, contact tracing, quarantining of suspected contacts, proper personal protection, safely conducted burials, improved education, social awareness and individual protective measures. Devising rigorous methodologies for the evaluation of the effectiveness of the control measures implemented to stop an outbreak is of paramount importance...
December 2018: Journal of Biological Dynamics
Camille Pouchol, Emmanuel Trélat
We analyse the asymptotic behaviour of integro-differential equations modelling N populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total number of individuals in each population. These models have already been shown to be suitable for the modelling of drug resistance in cancer, and they generalize the usual Lotka-Volterra ordinary differential equations. Our aim is to give conditions under which there is persistence of all species...
December 2018: Journal of Biological Dynamics
Aurelio A de Los Reyes V, Jose Maria L Escaner
Dengue is endemic in the Philippines and poses a substantial economic burden in the country. In this work, a compartmentalized model which includes healthcare-seeking class is developed. The reproduction number is determined to investigate critical parameters influencing transmission. Partial rank correlation coefficient (PRCC) technique is performed to address how the model output is affected by changes in a specific parameter disregarding the uncertainty over the rest of the parameters. Results show that mosquito biting rate, transmission probability from mosquito to human, respectively, from human to mosquito, and fraction of individuals who seek healthcare at the onset of the disease, posted high PRCC values...
December 2018: Journal of Biological Dynamics
Indrajit Ghosh, Pankaj Kumar Tiwari, Sandip Mandal, Maia Martcheva, Joydev Chattopadhyay
Global eradication of Guinea worm disease (GWD) is in the final stage but a mysterious epidemic of the parasite in dog population makes the elimination programme challenging. There is neither a vaccine nor an effective treatment against the disease and therefore intervention strategies rely on the current epidemiological understandings to control the spread of the disease. A novel mathematical model can predict the future outbreaks and it can quantify the dissemination rates of control interventions. Due to the lack of such novel models, a realistic mathematical model of GWD dynamics with human population, dog population, copepod population and the worm larvae is proposed and analyzed...
December 2018: Journal of Biological Dynamics
Hidekazu Yoshioka, Yuta Yaegashi
A new bio-economic model for managing population of non-renewable inland fishery resource in uncertain environment is presented. Population dynamics of the resource is described with stochastic differential equations (SDEs) having ambiguous growth and mortality rates. The performance index to be maximized by the manager of the resource while minimized by nature is presented in the context of differential game theory. The dynamic programming principle leads to a Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation that governs the optimal resource management strategy under the ambiguity...
December 2018: Journal of Biological Dynamics
Junyuan Yang, Yuming Chen
In this paper, we propose an SIVS epidemic model with continuous age structures in both infected and vaccinated classes and with a general nonlinear incidence. Firstly, we provide some basic properties of the system including the existence, uniqueness and positivity of solutions. Furthermore, we show that the solution semiflow is asymptotic smooth. Secondly, we calculate the basic reproduction number [Formula: see text] by employing the classical renewal process, which determines whether the disease persists or not...
December 2018: Journal of Biological Dynamics
Karly A Jacobsen, Mark G Burch, Joseph H Tien, Grzegorz A Rempała
We consider a Markovian SIR-type (Susceptible → Infected → Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model where edges in different layers correspond to potentially infectious contacts of different types. We assume that the graph structure evolves in response to the epidemic via activation or deactivation of edges of infectious nodes. We derive a large graph limit theorem that gives a system of ordinary differential equations (ODEs) describing the evolution of quantities of interest, such as the proportions of infected and susceptible vertices, as the number of nodes tends to infinity...
December 2018: Journal of Biological Dynamics
Aditya Sai, Nan Kong
Sparse grid interpolation is a popular numerical discretization technique for the treatment of high dimensional, multivariate problems. We consider the case of using time-series data to calibrate epidemiological models from both phenomenological and mechanistic perspectives using this computational tool. By capturing the dynamics underlying both global and local spaces, our algorithm identifies potentially optimal regions of the parameter space and directs computational effort towards resolving the dynamics and resulting fits of these regions...
December 2018: Journal of Biological Dynamics
Ahmed M Elaiw, Taofeek O Alade, Saud M Alsulami
In this paper, we study the stability analysis of latent Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modelled by a general nonlinear function which satisfies a set of conditions. The model is incorporated by intracellular discrete or distributed time delays. Using the method of Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.
December 2018: Journal of Biological Dynamics
Meng Bai, Shihe Xu
In this paper we study a two-phase size-structured population model with distributed delay in the birth process. This model distinguishes individuals by 'active' or 'resting' status. The individuals in the two life-stages have different growth rates. Only individuals in the 'active' stage give birth to the individuals in the 'active' stage or the 'resting' stage. The size of all the newborns is 0. By using the method of semigroups, we obtain that the model is globally well-posed and its solution possesses the property of asynchronous exponential growth...
December 2018: Journal of Biological Dynamics
Piotr Skupin, Mieczyslaw Metzger
The paper discusses the possibility of using a mixture of two growth limiting substrates to induce or eliminate self-sustained oscillations in a continuous culture process. The proportion of both substrates in the mixture is treated as a new control variable. The presented approach is based on the assumption that the oscillatory behaviour occurs for selected substrates in some range of dilution rates. Because a double-substrate limitation may occur, the analysis is performed for two fundamental substrate utilization patterns: simultaneous consumption and diauxic growth...
December 2018: Journal of Biological Dynamics
Sara Bernardi, Annachiara Colombi, Marco Scianna
The swarming of a bee colony is guided by a small group of scout individuals, which are informed of the target destination (the new nest). However, little is known on the underlying mechanisms, i.e. on how the information is passed within the population. In this respect, we here present a discrete mathematical model to investigate these aspects. In particular, each bee, represented by a material point, is assigned its status within the colony and set to move according to individual strategies and social interactions...
December 2018: Journal of Biological Dynamics
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