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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
Hui Miao, Zhidong Teng, Xamxinur Abdurahman
In this paper, the dynamical behaviours for a five-dimensional virus infection model with three delays which describes the interactions of antibody, cytotoxic T-lymphocyte (CTL) immune responses and Beddington-DeAngelis incidence are investigated. The reproduction numbers for virus infection, antibody immune response, CTL immune response, CTL immune competition and antibody immune competition, respectively, are calculated. By using the Lyapunov functionals and linearization method, the threshold conditions on the local and global stability of the equilibria for infection-free, immune-free, antibody response, CTL response and interior, respectively, are established...
December 2018: Journal of Biological Dynamics
Rui Xu, Xiaohong Tian, Shihua Zhang
In this paper, a within-host HIV-1 infection model with virus-to-cell and direct cell-to-cell transmission and explicit age-since-infection structure for infected cells is investigated. It is shown that the model demonstrates a global threshold dynamics, fully described by the basic reproduction number. By analysing the corresponding characteristic equations, the local stability of an infection-free steady state and a chronic-infection steady state of the model is established. By using the persistence theory in infinite dimensional system, the uniform persistence of the system is established when the basic reproduction number is greater than unity...
December 2018: Journal of Biological Dynamics
Michael Barfield, Maia Martcheva, Necibe Tuncer, Robert D Holt
This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model...
December 2018: Journal of Biological Dynamics
Wayne M Getz, Eric R Dougherty
Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity...
December 2018: Journal of Biological Dynamics
Benjamin J Ridenhour, Jerry R Ridenhour
Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system [Formula: see text] which arise as critical points of f, under the assumption that [Formula: see text] is positive semi-definite. It is shown that the condition [Formula: see text], where [Formula: see text] is the smallest eigenvalue of [Formula: see text], plays a key role in guaranteeing uniform asymptotic stability and in providing information on the basis of attraction of those equilibria.
December 2018: Journal of Biological Dynamics
Christian T K-H Stadtländer
No abstract text is available yet for this article.
December 2018: Journal of Biological Dynamics
Manli Jin, Yuguo Lin
In this paper, we consider a stochastic SIRS epidemic model with seasonal variation and saturated incidence. Firstly, we obtain the threshold of stochastic system which determines whether the epidemic occurs or not. Secondly, we prove that there is a non-trivial positive periodic solution if [Formula: see text].
December 2018: Journal of Biological Dynamics
T Berge, J M-S Lubuma, G M Moremedi, N Morris, R Kondera-Shava
We deal with the following question: Can the consumption of contaminated bush meat, the funeral practices and the environmental contamination explain the recurrence and persistence of Ebola virus disease outbreaks in Africa? We develop an SIR-type model which, incorporates both the direct and indirect transmissions in such a manner that there is a provision of Ebola viruses. We prove that the full model has one (endemic) equilibrium which is locally asymptotically stable whereas, it is globally asymptotically stable in the absence of the Ebola virus shedding in the environment...
December 2017: Journal of Biological Dynamics
Shihe Xu, Meng Bai, Fangwei Zhang
In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution...
December 2017: Journal of Biological Dynamics
(no author information available yet)
No abstract text is available yet for this article.
December 2017: Journal of Biological Dynamics
N S Ravindran, M Mohamed Sheriff, P Krishnapriya
A simple mathematical model for the growth of tumour with discrete time delay in the immune system is considered. The dynamical behaviour of our system by analysing the existence and stability of our system at various equilibria is discussed elaborately. We set up an optimal control problem relative to the model so as to minimize the number of tumour cells and the chemo-immunotherapeutic drug administration. Sensitivity analysis of tumour model reveals that parameter value has a major impact on the model dynamics...
December 2017: Journal of Biological Dynamics
Luis Sanz, Juan Antonio Alonso
In this work we develop approximate aggregation techniques in the context of slow-fast linear population models governed by stochastic differential equations and apply the results to the treatment of populations with spatial heterogeneity. Approximate aggregation techniques allow one to transform a complex system involving many coupled variables and in which there are processes with different time scales, by a simpler reduced model with a fewer number of 'global' variables, in such a way that the dynamics of the former can be approximated by that of the latter...
December 2017: Journal of Biological Dynamics
Glenn E Lahodny, Raju Gautam, Renata Ivanek
A number of environmentally transmitted infectious diseases are characterized by intermittent infectiousness of infected hosts. However, it is unclear whether intermittent infectiousness must be explicitly accounted for in mathematical models for these diseases or if a simplified modelling approach is acceptable. To address this question we study the transmission of salmonellosis between penned pigs in a grower-finisher facility. The model considers indirect transmission, growth of free-living Salmonella within the environment, and environmental decontamination...
December 2017: Journal of Biological Dynamics
Winston Garira
Modelling of infectious disease systems has entered a new era in which disease modellers are increasingly turning to multiscale modelling to extend traditional modelling frameworks into new application areas and to achieve higher levels of detail and accuracy in characterizing infectious disease systems. In this paper we present a categorization framework for categorizing multiscale models of infectious disease systems. The categorization framework consists of five integration frameworks and five criteria. We use the categorization framework to give a complete categorization of host-level immuno-epidemiological models (HL-IEMs)...
December 2017: Journal of Biological Dynamics
Alisa DeStefano, Clyde F Martin, Dorothy I Wallace
We present a model for the transport of a single type of asbestos fibre through the human body. The model captures the transport modes that pertain particularly to the lungs and the mesothelium. Numerical solutions of the system follow observed movement in the body. We compare the accumulation of fibres in the lungs versus the mesothelium, and then we give analysis and results for various cases of exposure level and exposure time. Models, such as the one developed here, can give clues as to how asbestos fibres impact the body, and where to look for major impact...
December 2017: Journal of Biological Dynamics
D Maxin, P Georgescu, L Sega, L Berec
Many models of mutualism have been proposed and studied individually. In this paper, we develop a general class of models of facultative mutualism that covers many of such published models. Using mild assumptions on the growth and self-limiting functions, we establish necessary and sufficient conditions on the boundedness of model solutions and prove the global stability of a unique coexistence equilibrium whenever it exists. These results allow for a greater flexibility in the way each mutualist species can be modelled and avoid the need to analyse any single model of mutualism in isolation...
December 2017: Journal of Biological Dynamics
Muhammad Zamir, Gul Zaman, Ali Saleh Alshomrani
This study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies, with quantifications of transmission and intervention parameters. To understand the nature of the initial transmission of the disease, the reproduction number [Formula: see text] is obtained by using the next-generation method...
December 2017: Journal of Biological Dynamics
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