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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
Virgilio Vázquez, Ignacio Barradas
In this paper we propose and discuss a simple two-dimensional model describing the interaction between two species: a plant population that gets pollinated by an insect population. The plants attract the insects deceiving them and not delivering any reward. We are interested in analysing the effect of learning by the insect population due to unsuccessfully visiting the deceiving plants. We are especially interested in three elements: conditions for the simultaneous coexistence of both species, their extinction as a function of the biological cost of the deceptiveness for the pollinator, and the appearance of oscillations in the dynamics...
December 2017: Journal of Biological Dynamics
Hong Xiang, Cheng-Cheng Zhu, Hai-Feng Huo
A drinking model with immigration is constructed. For the model with problem drinking immigration, the model admits only one problem drinking equilibrium. For the model without problem drinking immigration, the model has two equilibria, one is problem drinking-free equilibrium and the other is problem drinking equilibrium. By employing the method of Lyapunov function, stability of all kinds of equilibria is obtained. Numerical simulations are also provided to illustrate our analytical results. Our results show that alcohol immigrants increase the difficulty of the temperance work of the region...
December 2017: Journal of Biological Dynamics
Joseph Malinzi, Amina Eladdadi, Precious Sibanda
Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic non-linear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug...
December 2017: 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...
December 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
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