International Journal of Biomathematics

In this paper, we consider the backward Euler discretization derived from a continuous SIRS epidemic model, which contains a remaining problem that our discrete model has two solutions for infected population; one is positive and the other is negative. Under an additional positiveness condition on infected population, we show that the backward Euler discretization is one of simple discrete-time analogue which preserves the global asymptotic stability of equilibria of the corresponding continuous model.

We are concerned with the problem of characterizing the distribution of the maximum number of individuals alive during a fixed time interval in host–parasitoid models, which is shown to have a matrix exponential form. We present simple conditions on the rates of change of population sizes for the matrix exponential solution to be explicit or algorithmically tractable. A particularly appealing feature of our solution based on splitting methods is that it allows us to obtain global error control.

Chloroplasts are organelles found in plant cells that conduct photosynthesis. The subchloroplast locations of proteins are correlated with their functions. With the availability of a great number of protein data, it is highly desired to develop a computational method to predict the subchloroplast locations of chloroplast proteins. In this study, we proposed a novel method to predict subchloroplast locations of proteins using tripeptide compositions. It first used the binomial distribution to optimize the feature sets. Then the support vector machine was selected to perform the prediction of subchloroplast locations of proteins. The proposed method was tested on a reliable and rigorous dataset including 259 chloroplast proteins with sequence identity ≤ 25%. In the jack-knife cross-validation, 92.21% envelope proteins, 93.20% thylakoid membrane, 52.63% thylakoid lumen and 85.00% stroma can be correctly identified. The overall accuracy achieves 88.03% which is higher than that of other models. Based on this method, a predictor called ChloPred has been built and can be freely available from http://cobi.uestc.edu.cn/people/hlin/tools/ChloPred/. The predictor will provide important information for theoretical and experimental research of chloroplast proteins.

In this study, we consider two target-cell limited models with saturation type infection rate and intracellular delay: one without self-proliferation and the other with self-proliferation of activated CD4⁺T cells. We discuss about the local and global behavior of both the systems in presence and absence of intracellular delay. It is shown that the endemic equilibrium of a target-cell limited model would be unstable in presence and absence of intracellular delay only when self-proliferation of activated CD4⁺T cell is considered. Otherwise, all positive solutions converge to the endemic equilibrium or disease-free equilibrium depending on whether the basic reproduction ratio is greater than or less than unity. Our study suggests that amplitude of oscillation is negatively correlated with the constant input rate of CD4⁺T cell when intracellular delay is absent or low. However, they are positively correlated if the delay is too high. Amplitude of oscillation, on the other hand, is always positively correlated with the proliferation rate of CD4⁺T cell for all delay. Our mathematical and simulation analysis also suggest that there are many potential contributors who are responsible for the variation of CD4⁺T cells and virus particles in the blood plasma of HIV patients.

Predator–prey model with harvesting is well studied. The role of disease in such system has a great importance and cannot be ignored. In this study we have considered a predator–prey model with disease circulating in the predator population only and we have also considered harvesting in the prey and in the susceptible predator. We have studied the local stability, Hopf bifurcation of the model system around the equilibria. We have derived the ecological and the disease basic reproduction numbers and we have observed its importance in the community structure of the model system and in controlling disease propagation in the predator population. We have paid attention to chaotic dynamics for increasing the force of infection in the predator. Chaotic population dynamics can exhibit irregular fluctuations and violent oscillations with extremely small or large population abundances. In this study main objective is to show the role of harvesting in controlling chaotic dynamics. It is observed that reasonable harvesting on the prey and the susceptible predator prevents chaotic dynamics.

In this study we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyze a mathematical model that describes the dynamics of HIV infection among the immigrant youths and how parental care can minimize or prevent the spread of the disease in the population. We analyze the model with both screening control and parental care, then investigate its stability and sensitivity behavior. We also conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is globally asymptotically stable. We establish optimal strategies for the control of the disease with screening and parental care, and provide numerical simulations to illustrate the analytic results.

Human behavioral responses fundamentally influence the spread of infectious disease. In this paper, we study a discrete-time SIS epidemic process in random networks. Three forms of individual awareness, namely, local awareness, global awareness and contact awareness, are considered. The effect of awareness is to reduce the risk of infection. Based on the stability theory of matrix difference equation, we derive analytically the epidemic threshold. It is found that both local and contact awareness can raise the epidemic threshold, while the global awareness only decreases the epidemic prevalence. Our results are in line with a recent result using differential equation-based methods.

Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against measured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo (MCMC) methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identifiability: a basic SIR model, an influenza model with vaccination and treatment and a HIV–Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV–Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The presented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.

Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essential tremor are related to excessive synchronization of neurons. In the line of therapy, stimulations to these pathologically synchronized neurons should be capable of breaking synchrony. As the first step of designing an effective stimulation, we consider desynchronization problem of coupled limit-cycle oscillators ensemble. First, the desynchronization problem is redefined in a nonlinear output regulation framework. Then, we design an output regulator (stimulation) which forces limit-cycle oscillators to track exogenous sinusoidal references with different phases. The proposed stimulation is robust against variations of oscillators' frequencies. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.

In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.