Nonnegative Equilibrium Point Research Articles

Stability and computational analysis of Influenza-A epidemic model through double time delay

Delay factors demonstration has a significant role in controlling a strain of infectious disease instead of a pharmaceutical strategy. According to the World Health Organization (WHO), 3–5 million cases are reported annually and approximately 290,000 to 650,000 respiratory deaths annually. So, in the present study, we develop a delayed mathematical model based on delay differential equations (DDEs) for the influenza epidemic using a deterministic approach by introducing double delay parameters. The four distinct sub-populations are considered susceptible, exposed, infected, and recovered. For the rigorous analysis, the fundamental properties of the model like positivity, boundedness, existence, and uniqueness, were studied. The influenza-free equilibrium (IFE) and influenza-existing equilibrium (IEE), are the two nonnegative equilibrium points that the model demonstrates. Both locally and globally, the asymptotic stability of the equilibrium points of the model is established and shown under specific situations of reproduction number. Additionally, investigated the model's parameter sensitivity and determined the relative sensitivity of each parameter. Both standard and nonstandard methods—such as Euler, Runge-Kutta, and nonstandard finite difference with a delayed sense—are presented to make computational analysis support a dynamical analysis and the best visualization of results. The stability of the non-standard finite difference scheme is thoroughly analyzed around the steady states of the model. Additionally, the results show that the nonstandard finite difference approximation is an efficient, cost-effective method, independent of time step size, to solve such highly nonlinear and complex real-world problems.

Simulation and forecasting CTLs response effectualness against global dynamics of SARS-CoV-2/HIV coinfection

Quantifying the dynamical traits and harshness of SARS-CoV-2/HIV coinfection, a modified deterministic seven compartmental mathematical model is framed at cellular level encapsulating the interrelationships between epithelial cells (predominant target cells of COVID-19 infection), CD4+ T cells (target cells of HIV/AIDS infection), SARS-CoV-2 virions, HIV virions and HIV-specific CTL response. As a way to comprehend the kinetics of SARS-CoV-2/HIV coinfection and to provide prediction of model outcomes, the positivity, boundedness and existence conditions of the biologically feasible equilibrium points have been studied. The criteria of local stability and global stability of the coinfection system around the non-negative equilibrium points have been investigated and the analytical results are enhanced numerically. To measure the influence of the model parameters in SARS-CoV-2/HIV transmission dynamics, sensitivity analysis has been performed. Semi-relative sensitivity analysis demonstrates the maximum deviation of the concentration of infected epithelial cells due to changes in the model parameters and states that six parameters are most sensitive. The numerical simulation stipulates that the COVID-19 infection is likely to be died out from a HIV patient body by increasing the apoptosis of infected epithelial cells and that is possible through the proliferation of the CD4+ T cells count of an individual living with HIV via antiretroviral therapy (ART). Additionally, elevated concentration of CD4+ T cells in people living with HIV assists in heightening the CTLs response to combat COVID-19 and other opportunistic infections.

MODEL PENYEBARAN KRIMINALITAS DENGAN PENGARUH KEBIJAKAN KRIMINAL SEBAGAI PENCEGAHAN PADA SITUASI KRISIS EKONOMI

Crime is behavior that violates the law and social norms so that people oppose it which can occur due to environmental factors, namely the imitation of criminality and individual economic factors, can be prevented by criminal policies, and can increase in certain situations, one of which is the economic crisis. The mathematical model of the spread of crime is built by considering individual economic factors which are implemented as work and non-work compartments, crime imitation factors which are implemented as the rate of crime affected, and criminal policy factors as an obstacle to crime. Based on the model that has been built, the equilibrium point and its stability, the basic reproduction rate, population dynamics, and conditions that can describe the influence of criminal policy and the economic crisis on the crime rate are determined. The model has one non-endemic equilibrium point and one non-negative endemic equilibrium point which can reach a stable condition. Numerical simulations show that population dynamics using parameter values and initial compartments obtained from various sources are stable towards an endemic equilibrium point, criminal policies can reduce crime rates, and economic crises can increase crime rates.

Analysis Dynamics Two Prey of a Predator-Prey Model with Crowley–Martin Response Function

The predator-prey model has been extensively developed in recent research. This research is an applied literature study with a proposed dynamics model using the Crowley–Martin response function, namely the development of the Beddington-DeAngelis response function. The aim of this research is to construct a mathematical model of the predator-prey model, equilibrium analysis and population trajectories analysis. The results showed that the predator-prey model produced seven non-negative equilibrium points, but only one equilibrium point was tested for stability. Stability analysis produces negative eigenvalues indicating fulfillment of the Routh-Hurwitz criteria so that the equilibrium point is locally asymtotically stable. Analysis of the stability of the equilibrium point indicates stable population growth over a long period of time. Numerical simulation is also given to see the trajectories of the population growth movement. The population growth of first prey and second prey is not much different, significant growth occurs at the beginning of the growth period, while after reaching the peak the trajectory growth slopes towards a stable point. Different growth is shown by the predator population, which grows linearly with time. The growth of predators is very significant because predators have the freedom to eat resources. Various types of trajectory patterns in ecological parameters show good results for population growth with the given assumptions.

Dynamical analysis of a [formula omitted] epidemic-like propagation model with non-smooth control

The continuous acceleration of information communication makes the spread of rumors constantly develop and change. Analysis of the dynamics of rumor propagation allows for its better control. In this paper, we study a rumor transmission model with a nonlinear transmission rate and a non-smooth threshold transmission function, based on the classical SI infectious disease model. In this model, we first prove the existence of the model solutions, and then obtain the number of non-negative equilibrium points. By dividing the model into spatially homogeneous and inhomogeneous parts with continuous and discontinuous, we discuss the characteristic equations of the equilibrium points and obtain the existence conditions for Saddle–node bifurcation, Turing bifurcation and Hopf bifurcation under the corresponding conditions. Finally, the feasibility of the theoretical calculation results is further verified by using the simulation results.

Stability analysis for single linkage class chemical reaction networks with distributed time delays⋆

In the present paper, we show two results concerning stability for a class of single linkage class chemical reaction networks (CRNs) with distributed time delays, all complexes of which are distinct. The dynamics of concentrations of species of the CRN with mass action kinetics (MAK) are described by the functional differential equations (FDEs) with distributed time delays for each reaction. As the first result, we show that any positive solution to the FDE of weakly reversible CRN globally converges to a positive equilibrium point in the functional state space. As the second result, we prove that any positive solution to the FDE of non-weakly reversible CRNs globally converges to a non-negative equilibrium point on the boundary of the positive orthant by decomposing the whole network into weakly reversible subnetworks and analyzing the stability of each subnetwork.

Mathematical Model for the Control of Unemployment on Ghana’s Labour Market

Unemployment is one of the major socioeconomic issues across the globe in which Ghana is no exception. The unavailability of jobs and its creation as being searched by persons belonging to the labour force actively looking for jobs makes the problem escalate rapidly in a growing economy. In this seven state model, we analysed into the three main economic sectors of Ghana to investigate how unemployment, employment, and newly created vacancy creation behave at equilibrium on the three economic sector levels. Moreover, we analysed how in a specific sector, the dynamics of the state variables control unemployment. Further analyses on the parameters indicated that, an increase in the rate of newly created vacancies results in a decrease in the number of unemployed persons and an increase in the number of employed. We assumed that a jobless person who is available for work but fails to make an effort to seek work is not part of the unemployed class among others. It was established that the model has one nonnegative equilibrium point. Lastly, we analyse the impact of perturbation of some parameters on the number of the unemployed and employed persons at equilibrium.unemployment

Novel global exponential stability results for a class of two-coupled-hub nonlinear genetic regulatory networks with time-varying delays

This work studies global exponential stability analysis for a class of nonlinear genetic regulatory networks (GRNs) with two-coupled-hub structure and time-varying delays. It is important to study the influence of hub genes in GRNs problem, due to there is the complexity arising from the interactions among hub gene nodes. In this article, the existence of GRN’s nonnegative equilibriums is presented and a sufficient condition such that all nonnegative equilibriums are positive can be further proved. In addition, novel global exponential stability (GES) criteria of coupled nonlinear GRN is established based on a Metzler matrix method. Furthermore, under the proposed delay-dependent and -independent GES sufficient conditions, it proves the considered GRNs has a unique non-negative GES equilibrium point. Compared with the existing GES criteria, it is worth stressing that the proposed GES conditions are easily verified by computing relative matrices eigenvalues and induced norms. Finally, the validity of the theoretical results is verified by three simulation examples.

Bifurcation Analysis of a Reaction–Diffusion Rumor Spreading Model with Nonsmooth Control

Rumors may cause serious harm to social productivity and life. Studying the dynamics of rumor propagation can help provide corresponding countermeasures to control communication effectively. Based on the classic [Formula: see text] infectious disease model, this paper studies a rumor spreading model with a time delay caused by communication delay between rumor communicators and nonsmooth threshold propagation function in reality. In this model, we solve non-negative equilibrium points firstly. By analyzing the characteristic equations of smooth and nonsmooth rumor systems, we establish local stability at non-negative equilibrium points and find the existence of Hopf bifurcation from two aspects of diffusion coefficient and delay, respectively. In addition, considering the discontinuity of rumor system, we separate it into two systems and get the condition of Hopf bifurcation when the system is discontinuous. We further verify the feasibility of the theoretical results by simulation results.

Dynamics Twin Cannibalism of Two Predator and Two Prey System with Prey Defense

The study discusses the condition of the existence of all non-negative equilibrium points. There are 9 realistic equilibrium points from the constructed model. A local stable condition is obtained, a point of equilibrium that is completely biologically feasible. The analytical method on the mathematically formed model is limited, so numerical simulation is also given to explore the model. Numerical simulation is intervened in a model that will show growth in trajectories. The tendency of trajectories in prey one and predator one species is relatively the same because the interactions that occur are intensive. Likewise, prey two and predator two occur, and the interactions that occur cause population growth grow to fluctuate. Differences occur in both types of species, namely predator-prey one and predator-prey two. In the one interaction group, growth tends to be more volatile and moves slowly towards the point of stability in population growth. Incidence is inversely proportional to the interaction of species two which tend to be faster towards the stability point. In general, the results of numerical simulations show that there is a pattern formation in the predator-prey system that grows sustainabley.

A system of two competitive prey species in presence of predator under the influence of toxic substances

In this article, a two prey - one predator model has been studied where two prey species are competitive in nature and also uses toxic substances for own existence. Biologically well posedness of the model system has been shown through positivity and boundedness of solutions. Existence criterion and stability analysis of the non-negative equilibrium points have been discussed. The sufficient conditions for existence of Hopf bifurcation and stability switches induced by delay are investigated. The direction and the stability criteria of the bifurcating periodic solutions are determined with the help of the normal form theory and the center manifold theorem. Numerical simulations are performed to illustrate the theoretical analysis results.

Mathematical Modelling of Deforestation Due to Population Density and Industrialization

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

SY2-3. The role of autophagy in pathophysiology of PE

The coupled repressilators, as a special case of cyclic genetic regulatory networks, can be used to adjust oscillations at the cellular level, and hence it have received extensive attention from many scholars. This paper addresses the problem of global exponential stability analysis for nonnegative equilibrium points of a class of coupled repressilator models with multiple time-varying delays. Sufficient conditions are investigated to guarantee that the considered model has a unique nonnegative equilibrium point which is globally exponentially stable. The obtained criteria are composed of several simple linear inequalities that are only related to the model parameters, so they can be easily verified by using the standard software tools. The results of two illustrative examples present the effectiveness of the proposed approach.

Mathematical modeling of diabetes and its restrain

In this paper, we have developed a mathematical model of diabetes (type-2 diabetes) in a deterministic approach. We have described our model in the population dynamics with four compartments. Namely, Susceptible, Imbalance Glucose Level (IGL), Treatment and Restrain population. Our model exhibits two nonnegative equilibrium points namely Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The expression for the Treatment reproduction number [Formula: see text] is computed. We have proved that the equilibrium points of the model are locally and globally asymptotically stable under some conditions. Numerical simulation is performed to verify our analytical findings such as stability of DFE and EE. The simulations show better results based on the required conditions. We tried to fit our model with the data given by the International Diabetes Federation (IDF) [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)] and it suits well with the data. It has been found that our model shows the decrease in diabetes-affected population compared with the data given by the IDF [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)].

Mathematical modeling and analysis of anemia during pregnancy and postpartum.

Anemia is a significant public health problem worldwide especially among pregnant women in low- and middle-income countries. In this study, a mathematical model of the population dynamics of anemia during pregnancy and postpartum is constructed. In the modeling process, four independent variables have been considered: (1) the numbers of nonpregnant nonanemic women, (2) anemic nonpregnant women, (3) anemic pregnant or postpartum women and (4) anemic pregnant or postpartum women with complications. The mathematical model is governed by a system of first-order ordinary differential equations. The stability analysis of the model is conducted using Routh-Hurwitz criteria. There is one nonnegative equilibrium point which is asymptotically stable. The equilibrium point obtained indicates the influential parameters that can be controlled to minimize the number of patients at each stage. The proposed model can be employed to forecast the future incidence and prevalence of the disease and appraise intervention programs.

Global Exponential Stability Analysis for A Class of Coupled Cyclic Genetic Regulatory Networks with Multiple Time-Varying Delays

The coupled repressilators, as a special case of cyclic genetic regulatory networks, can be used to adjust oscillations at the cellular level, and hence it have received extensive attention from many scholars. This paper addresses the problem of global exponential stability analysis for nonnegative equilibrium points of a class of coupled repressilator models with multiple time-varying delays. Sufficient conditions are investigated to guarantee that the considered model has a unique nonnegative equilibrium point which is globally exponentially stable. The obtained criteria are composed of several simple linear inequalities that are only related to the model parameters, so they can be easily verified by using the standard software tools. The results of two illustrative examples present the effectiveness of the proposed approach.

Stability Analysis of Prey-Predator Model With Holling Type IV Functional Response and Infectious Predator

Stability of equilibrium points of the prey-predator model with diseases that spreads in predators where the predation function follows the simplified Holling type IV functional response are investigated. To find out the local stability of the equilibrium point of the model, the system is then linearized around the equilibrium point using the Jacobian matrix method, and stability of the equilibrium point is determined via the eigenvalues method. There exists three non-negative equilibrium points, except , that may exist and stable. Simulation results show that with the variation of several parameter values infection rate of disease , the diseases in the system may become endemic, or may become free from endemic.

Impacts of strong Allee effect and hunting cooperation for a Leslie-Gower predator-prey system

In this paper, we propose a Leslie-Gower predator-prey system with strong Allee effect in prey and hunting cooperation among predators. To discuss the impacts of Allee effect and hunting cooperation, we choose the severity of Allee effect and the cooperative hunting coefficient as the main control parameters. First, using the topology equivalent method, type of singular point (0,0) is obtained. Moreover, the basin of attraction of (0,0) is studied. Then, the stability of all nonnegative equilibrium points, including type of degenerate equilibrium point, is discussed. Based on Sotomayor’s theorem, the existence of saddle-node bifurcation is derived. To determine the stability of limit cycles arising from the Hopf bifurcation, the first Lyapunov number is calculated. Meanwhile, by the rigorous mathematical proofs, we obtain that the bifurcating limit cycle is stable if the hunting cooperation coefficient and the severity of Allee effect are sufficiently small. Finally, numerical simulations are presented to validate the theoretical results and further explore the influences of Allee effect and hunting cooperation. These results show that strong Allee effect and hunting cooperation have significant impacts on dynamical behaviors of the system.

Modeling the Control of Zika Virus Vector Population Using the Sterile Insect Technology

This work is aimed at formulating a mathematical model for the control of mosquito population using sterile insect technology (SIT). SIT is an environmental friendly method, which depends on the release of sterile male mosquitoes that compete with wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring. The basic offspring number of the mosquitoes’ population was computed, after which we investigated the existence of two equilibrium points of the model. When the basic offspring number of the model M0, is less than or equal to 1, a mosquito extinction equilibrium point E2, which is often biologically unattainable, was shown to exits. On the other hand, if M0>1, we have the nonnegative equilibrium point E1 which is shown to be both locally and globally asymptotically stable whenever M0>1. Local sensitivity analysis was then performed to know the parameters that should be targeted by control intervention strategies and result shows that female mating probability to be with the sterile male mosquitoes ρS, mating rate of the sterile mosquito β2, and natural death rates of both aquatic and female mosquitoesμA+μF have greater impacts on the reduction and elimination of mosquitoes from a population. Simulation of the model shows that enough release of sterile male mosquitoes into the population of the wild mosquitoes controls the mosquito population and as such can reduce the spread of mosquito borne disease such as Zika.

Development and Analysis of a Mathematical Model for the Population Dynamics of Diabetes Mellitus During Pregnancy

Diabetes Mellitus (DM) during pregnancy is a major global public health burden with various adverse outcomes. In this paper, a mathematical model of the population dynamics of DM during pregnancy is developed and analyzed. Four independent variables have been considered, namely the numbers of nonpregnancy nondiabetic women, diabetic nonpregnant women, diabetic pregnant women and diabetic pregnant women with complication. The model is described by a system of ordinary differential equations. The stability of the equilibrium point is analyzed using Routh-Hurwitz criteria. The model is numerically simulated using MATLAB to verify the analytical results. The model has only one nonnegative equilibrium point which is asymptotically stable. The equilibrium solution is further investigated using simple sensitivity analysis. The results of simple sensitivity analysis of the equilibrium solution suggest the key parameters of the model. The equilibrium point of the model indicates the influential parameters that can be controlled to address the issue.