International Journal of Biomathematics

Accurate estimate of tree biomass is essential for forest management. In recent years, several climate-sensitive allometric biomass models with diameter at breast height $(D)$ as a predictor have been proposed for various tree species and climate zones to estimate tree aboveground biomass (AGB). But the allometric models only account for the potential effects of climate on tree biomass and do not simultaneously explain the influence of climate on $D$ growth. In this study, based on the AGB data from 256 destructively sampled trees of three larch species randomly distributed across the five secondary climate zones in northeastern and northern China, we first developed a climate-sensitive AGB base model and a climate-sensitive $D$ growth base model using a nonlinear least square regression separately. A compatible simultaneous model system was then developed with the climate-sensitive AGB and $D$ growth models using a nonlinear seemingly unrelated regression. The potential effects of several temperature and precipitation variables on AGB and $D$ growth were evaluated. The fitting results of climatic sensitive base models were compared against those of their compatible simultaneous model system. It was found that a decreased isothermality ([mean of monthly (maximum temperature-minimum temperature)]/(Maximum temperature of the warmest month-Minimum temperature of the coldest month)) and total growing season precipitation, and increased annual precipitation significantly increased the values of AGB; an increase of temperature seasonality (a standard deviation of the mean monthly temperature) and precipitation seasonality (a standard deviation of the mean monthly precipitation) could lead to the increase of $D$. The differences of the model fitting results between the compatible simultaneous system with the consideration of climate effects on both AGB and $D$ growth and its corresponding climate-sensitive AGB and $D$ growth base models were very small and insignificant $(p>0.05)$. Compared to the base models, the inherent correlation of AGB with $D$ was taken into account effectively by the proposed compatible model system developed with the climate-sensitive AGB and $D$ growth models. In addition, the compatible properties of the estimated AGB and $D$ were also addressed substantially in the proposed model system.

Since 1921, the Bacille Calmette–Guerin (BCG) vaccine continues to be the most widely used vaccine for the prevention of Tuberculosis (TB). However, the immunity induced by BCG wanes out after some time making the vaccinated individual susceptible to TB infection. In this work, we formulate a mathematical model that incorporates the vaccination of newly born children and older susceptible individuals in the transmission dynamics of TB in a population, with a vaccine that can confer protection on older susceptible individuals. In the absence of disease-induced deaths, the model is shown to undergo the phenomenon of backward bifurcation where a stable disease-free equilibrium (DFE) co-exists with a stable positive (endemic) equilibrium when the associated reproduction number is less than unity. It is shown that this phenomenon does not exist in the absence of imperfect vaccine, exogenous reinfection, and reinfection of previously treated individuals. It is further shown that a special case of the model has a unique endemic equilibrium point (EEP), which is globally asymptotically stable when the associated reproduction number exceeds unity. Uncertainty and sensitivity analysis are carried out to identify key parameters that have the greatest influence on the transmission dynamics of TB in the population using the total population of latently infected individuals, total number of actively infected individuals, disease incidence, and the effective reproduction number as output responses. The analysis shows that the top five parameters of the model that have the greatest influence on the effective reproduction number of the model are the transmission rate, the fraction of fast disease progression, modification parameter which accounts for reduced likelihood to infection by vaccinated individuals due to imperfect vaccine, rate of progression from latent to active TB, and the treatment rate of actively infected individuals, with other key parameters influencing the outcomes of the other output responses. Numerical simulations suggest that with higher vaccination rate of older susceptible individuals, fewer new born children need to be vaccinated, in order to achieve disease eradication.

In this paper, we construct a mathematical model to investigate the interaction between the tumor cells, the immune cells and the helper T cells (HTCs). We perform mathematical analysis to reveal the stability of the equilibria of the model. In our model, the HTCs are stimulated by the identification of the presence of tumor antigens. Our investigation implies that the presence of tumor antigens may inhibit the existence of high steady state of tumor cells, which leads to the elimination of the bistable behavior of the tumor-immune system, i.e. the equilibrium corresponding to the high steady state of tumor cells is destabilized. Choosing immune intensity $c$ as bifurcation parameter, there exists saddle-node bifurcation. Besides, there exists a critical value $c_{\ast }$, at which a Hopf bifurcation occurs. The stability and direction of Hopf bifurcation are discussed.

We present a statistical distribution of a nanorobot motion inside the blood. This distribution is like the distribution of A and B particles in continuous time random walk scheme inside the fluid reactive anomalous transport with stochastic waiting time depending on the Gaussian distribution and a Gaussian jump length which is detailed in Zhang and Li [J. Stat. Phys., Published Online with https://doi.org/10.1007/s10955-018-2185-8, 2018]. Rather than estimating the length parameter of the jumping distance of the nanorobot, we normalize the Probability Density Function (PDF) and present some reliability properties for this distribution. In addition, we discuss the truncated version of this distribution and its statistical properties, and estimate its length parameter. We use the estimated distance to study the conditions that give a finite expected value of the first meeting time between this nanorobot in the case of nonlinear flow with independent $d$-dimensional Gaussian jumps and an independent $d$-dimensional CD4 T Brownian cell in the blood ($d$-space) to prevent the HIV virus from proliferating within this cell.

Dengue is an acute arthropode-borne virus, belonging to the family Flaviviridae. Currently, there are no vaccines or treatments available against dengue. Thus it is important to understand the dynamics of dengue in order to control the infection. In this paper, we study the long-term dynamics of the model that is presented in [S. D. Perera and S. S. N. Perera, Simulation model for dynamics of dengue with innate and humoral immune responses, Comput. Math. Methods Med. 2018 (2018) 8798057, 18 pp. https://doi.org/10.1155/2018/8798057] which describes the interaction of virus with infected and uninfected cells in the presence of innate and humoral immune responses. It was found the model has three equilibria, namely: infection free equilibrium, no immune equilibrium and endemic equilibrium, then analyzed its stability analytically. The analytical findings of each model have been exemplified by numerical simulations. Given the fact that intensity of dengue virus replication at early times of infection could determine clinical outcomes, it is important to understand the impact of innate immunity, which is believed to be the first line of defense against an invading pathogen. For this we carry out a simulation case study to investigate the importance of innate immune response on dengue virus dynamics. A comparison was done assuming that innate immunity was active; innate immunity was in quasi-steady state and innate immunity was inactive during the virus replication process. By a further analysis of the qualitative behavior of the quasi-steady state, it was observed that innate immune response plays a pivotal role in dengue virus dynamics. It can change the dynamical behavior of the system and is essential for the virus clearance.

In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species, we study a mutualistic model on a periodically evolving domain. To overcome the difficulty caused by the advection and dilution terms, we transform the model to a reaction–diffusion problem in a fixed domain. By means of eigenvalue problems, the threshold parameters are introduced. The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method. The impact of the domain evolution rate on the persistence or extinction of species is analyzed. Numerical simulations are performed to illustrate our analytical results.

In this paper, we study some models with repulsion effect on superinfecting viruses by infected cells

Bipolar disorder is a neurological disorder that consists of two main factors, i.e. mania and depression. There are two main drawbacks in clinical diagnosis of the bipolar disorder. First, bipolar disorder is mostly wrongly diagnosed as unipolar depression in clinical diagnosis. This is, because in clinical diagnosis, the first factor is often neglected due to its approach toward positivity. Consequently, the element of bipolarity vanishes and the disease becomes worse. Second, the types of bipolar disorder are mostly misdiagnosed due to similar symptoms. To overcome these problems, the bipolar fuzzy soft set (BFS-set) and bipolar fuzzy soft mappings (BFS-mappings) are useful to tackle bipolarity and to construct a strong mathematical modeling process to diagnose this disease correctly. This technique is extensive but simple as compared to existing medical diagnosis methods. A chart (relation between different types and symptoms of bipolar disorder) is provided which contains different ranges over the interval $[-1,1]$. A process of BFS-mappings is also provided to obtain correct diagnosis and to suggest the best treatment. Lastly, a generalized BFS-mapping is introduced which is helpful to keep patient’s improvement record. The case study indicates the reliability, efficiency and capability of the achieved theoretical results. Further, it reveals that the connection of soft set with bipolar fuzzy set is fruitful to construct a connection between symptoms which minimize the complexity of the case study.

This paper is concerned with the minimal wave speed in a diffusive epidemic model with nonlocal delays. We define a threshold. By presenting the existence and the nonexistence of traveling wave solutions for all positive wave speed, we confirm that the threshold is the minimal wave speed of traveling wave solutions, which models that the infective invades the habitat of the susceptible. For some cases, it is proven that spatial nonlocality may increase the propagation threshold while time delay decreases the threshold.

It is of crucial significance to study the infectious disease phenomenon by using the SIRS model and thoughts of Julia set. In this paper, Julia set of the discrete version of the SIRS model is established to analyze the fractal dynamics of this model. Then, controller is designed to change the Julia set. Furthermore, the box-counting dimensions of the controlled Julia sets by selecting different appropriate parameters are computed to show the complexity of the model. Finally, a nonlinear coupling method is introduced to synchronize the Julia sets with different parameters of the same system. Simulation results show the efficacy of these methods.