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In this paper, a single-species logistic model with both fear effect-type feedback control and additive Allee effect is developed and investigated using the new coronavirus as a feedback control variable. When the system introduces additive Allee effect and fear effect-type feedback control, more complicated dynamical behavior is obtained. The system can undergo transcritical bifurcation, saddle-node bifurcation, degenerate Hopf bifurcation and Bogdanov–Takens bifurcation. By numerical simulations, the system exhibits homoclinic bifurcation and saddle-node bifurcation of limit cycles as parameters are altered. Remarkably, it is the first time that two limit cycles have been discovered in a single-species logistic model with the Allee effect. Further, stronger Allee effect or stronger fear effect can lead to the extinction of the species population.

Here, we apply multi team concept to the prey-predator model. The prey teams help each other. Local stability of the system is studied. Global stability and persistence of the model without help are investigated.

Bus and metro are the two most important public transport modes in many metropolises in China, and they both have experienced rapid growth and meanwhile coexisted for decades. However, little is known on how the metro and bus interacted with each other during their rapid growths. This study was proposed to investigate the growth and interaction of bus-metro from the macro perspective. The passenger volume data for metro and bus were collected from seven central cities to represent the development of the two public transport modes, and the Logistic model and Lotka–Volterra model were employed to model the growth as well as the interaction of bus-metro, respectively. The modeling results show that the development of bus conforms to the Logistic model (i.e. S-shaped curve), while the bus-metro interaction conforms to the Lotka–Volterra model with interaction modes of competition (Shanghai city from 2000–2009, Shanghai city from 2009–2018, Guangzhou city from 2009–2017, Nanjing city from 2008–2018), and mutualism (Guangzhou city from 2000–2009). The further analysis indicates that urban characteristics and policies determine the interaction, and the parameters of the Lotka–Volterra model could be used to judge the bus-metro interaction type.

We study the dynamics of stochastically forced 2D logistic-type discrete model. Under random disturbances, stochastic trajectories leaving deterministic attractors can form complex dynamic regimes that have no analogue in the deterministic case. In this paper, we analyze an impact of the random noise on 2D logistic-type model in the bistability zones with coexisting attractors (equilibria, closed invariant curves, discrete cycles). For the constructive probabilistic analysis of the random states distribution around such attractors, a stochastic sensitivity functions technique and method of confidence domains are used. For the considered model, on the base of the suggested approach, a phenomenon of noise-induced transitions between attractors and the generation of chaos are analyzed.

This paper aims to study the dynamic behavior of a logistic model with feedback control and Allee effect. We prove the origin of the system is always an attractor. Further, if the feedback control variable and Allee effect are big enough, the species goes extinct. According to the analysis of the Jacobian matrix of the corresponding linearized system, we obtain the threshold condition for the local asymptotic stability of the positive equilibrium point. Also, we study the occurrence of saddle-node bifurcation, supercritical and subcritical Hopf bifurcations with the change of parameter. By calculating a universal unfolding near the cusp and choosing two parameters of the system, we can draw a conclusion that the system undergoes Bogdanov–Takens bifurcation of codimension-2. Numerical simulations are carried out to confirm the feasibility of the theoretical results. Our research can be regarded as a supplement to the existing literature on the dynamics of feedback control system, since there are few results on the bifurcation in the system so far.

In this paper, SIS and SIRS models for carrier dependent infectious diseases with immigration are proposed and analyzed by considering effects of environmental and human population related factors which are conducive to the growth of carrier population. In the modeling process, the density of carrier population is governed by a general logistic model. Further, it is assumed that the growth rate per capita and the modified carrying capacity of carrier population increase as the human population density increases. In each case, it is shown that the spread of an infectious disease increases as the carrier population density increases and the disease becomes more endemic due to immigration.

This study presents diffusion processes methodology on tree diameter distribution problem. We use stochastic differential equation methodology to derive a univariate age-dependent probability density function of a tree diameter distribution. The purpose of this paper is to investigate the relationship between the stochastic linear and logistic shape diameter growth models and diameter distribution laws. We establish the probabilistic characteristics of stochastic growth models, such as the univariate transition probability density of tree diameter, the mean and variance of tree diameter. We carry out comparison of proposed continuous time stochastic models on the basis of Hong-Li, Gini, Shapiro-Wilk goodness-of-fit statistics and normal probability plot. Parameter estimations are based on discrete observations over age of trees. To model the tree diameter distribution, as an illustrative experience, a real data set from repeated measurements on a permanent sample plot of pine (Pinus sylvestris) stand in the Kazlu Ruda district at Lithuania is used. The results are implemented in the symbolic computational language MAPLE.

A framework for interpretation of classical populations dynamics models written in terms of ordinary differential equations and related to biological mechanisms is proposed. This approach is based on the construction of functional schemes, similar to those used to symbolize chemical reactions. These schemes can be associated to differential equations which formalize the kinetics of these reactions. So schemes associated to classical one-species models are given (exponential, logistic, Gompertz, and Kostitzin models). Some typical cases of two species models proposed by Lotka and Volterra (predator-prey and competition models) are also explored.

One of the major challenges in population economics is accurately predicting population size. Incorrect predictions can lead to ineffective population control policies. Traditional differential models assume a smooth change in population, but this assumption is invalid when measuring population on a small-time scale. To address this change, we developed two-scale fractal population dynamics that can accurately predict population size with minimal experimental data. The Taylor series method is used to reveal the population’s dynamical properties, and the Padé technology is adopted to accelerate the convergence rate.

This paper proposes the use of the maximum entropy principle to construct a probability model under constraints for the analysis of dichotomous data using the odds ratio adjusted for covariates. It gives a new understanding of the now famous logistic model. We show that we can do away with the hypothesis of linearity of the log odds and still effectively use the model properly. From a practical point of view, the result implies that we do not have to discuss the plausability of the linearity hypothesis relative to the data or the phenomenon under study. Hence, when using the logistic model, we do not have to discuss the multiplicative effect of the covariates on the odds ratio. This is a major gain in the use of the model if one does not have to establish or justify the multiplicative effect, for instance, of alcohol consumption while considering low birth weight babies.

We studied the effect of additive and multiplicative noises on the growth of a tumor based on a logistic growth model. The steady-state probability distribution and the average population of the tumor cells were given to explain the important roles of correlated noises in the tumor growth. We explored that multiplicative noise induces a phase transition of the tumor growth from a uni-stable state to a bi-stable state; the relationship between the intensity of multiplicative noise and the population of the tumor cells shows a stochastic resonance-like characteristic. It was also confirmed that additive noise weakened rather than extinguish the tumor growth. Homologous noises, however, promote the growth of a tumor. We also discussed about the relationship between the tumor treatment and the model.

The Malaysian economy suffered serious consequences from the 1997 Asian financial crisis. As a consequence, many listed companies became financially distressed due to mounting debts, huge accumulated losses, and poor cash flows. Under the provisions of Practice Note 4/2001 (PN4), issued by the Bursa Malaysia on February 15, 2001, 91 public listed companies, after fulfilling the criteria of PN4, were classified as financially distressed companies. Financial distress precedes bankruptcy; however, not all financially distressed companies will end up in bankruptcy. The main purpose of this paper is to use financial variables to predict potential financially distressed firms using the logistic regression model. Then the predictive ability of the prediction model was analyzed and the findings are encouraging and consistent for the sample analyzed and the period of study.

We formulate a two-gender susceptible–infectious–susceptible (SIS) model to search for optimal childhood and catch-up vaccines over a 20-year period. The optimal vaccines should minimize the cost of Human Papillomavirus (HPV) disease in random logistically growing population. We find the basic reproduction number $R_0$ for the model and use it to describe the local-asymptotic stability of the disease-free equilibrium (DFE). We estimate the solution of the model to show the role of vaccine in reducing $R_0$ and controlling the disease. We formulate some optimal control problems to find the optimal vaccines needed to control HPV under limited resources. The optimal vaccines needed to keep $R_0\le 1$ are the catch-up vaccine rates of 0.004 and 0.005 for females and males, respectively; 100$\%$ is needed to reduce $R_0$ to its minimum value. To reduce the expenses for HPV disease and its vaccines, we need 100$\%$ childhood vaccines (both genders) for the first 13–14 years and then gradually reduce the vaccine to reach $0\%$ at year 20. For adults (both genders), we need maximum rates (one) for the first 9 years, then $0.2$ for the next 3–4 years before reducing gradually to zero rate at year 20. Although the childhood vaccines provide very early protection strategy against HPV, its time to control HPV is longer than that for adult vaccines. Thus, full adults’ only vaccines for enough period is a viable choice to control HPV at minimal cost and short time.