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Showing papers in "International Journal of Biomathematics in 2022"


Journal ArticleDOI
TL;DR: In this article , the authors formulated the transmission phenomena of dengue infection with vaccination, treatment and reinfection via Atangana-Baleanu operator to thoroughly explore the intricate system of the disease.
Abstract: The infection of dengue is an intimidating vector-borne disease caused by a pathogenic agent that affects different temperature areas and brings many losses in human health and economy. Thus, it is valuable to identify the most influential parameters in the transmission process for the control of dengue to lessen these losses and to turn down the economic burden of dengue. In this research, we formulate the transmission phenomena of dengue infection with vaccination, treatment and reinfection via Atangana–Baleanu operator to thoroughly explore the intricate system of the disease. Furthermore, to come up with more realistic, dependable and valid results through fractional derivative rather than classical order derivative. The next-generation approach has been utilized to compute the basic reproduction number for the suggested fractional model, indicated by [Formula: see text]; moreover, we conducted sensitivity test of [Formula: see text] to recognize and point out the role of parameters on [Formula: see text]. Our numerical results predict that the reproduction number of the system of dengue infection can be controlled by controlling the index of memory. The uniqueness and existence result has been proved for the solution of the system. A novel numerical method is presented to highlight the time series of dengue system. Eventually, we get numerical results for different assumptions of [Formula: see text] with specifying factors to conceptualize the effect of [Formula: see text] on the dynamics. It has been noted that the fractional-order derivative offers realistic, clear-cut and valid information about the dynamics of dengue fever. Moreover, we note through our analysis that the input parameters’ index of memory, biting rate, transmission probability and recruitment rate of mosquitos can be used as control parameter to lower the level of infection.

11 citations


Journal ArticleDOI
TL;DR: In this paper , a discretized two-dimensional Phytoplankton-Zooplon model is investigated and the results for the existence and uniqueness, and conditions for local stability with topological classifications of the equilibrium solutions are determined.
Abstract: Phytoplanktons are drifting plants in an aquatic system. They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis. Zooplanktons are drifting animals found inside the aquatic bodies. For stable aquatic ecosystem, the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras, there has been a universal explosion in destructive Plankton or algal blooms. Many investigators used various mathematical methodologies to try to explain the bloom phenomenon. So, in this paper, a discretized two-dimensional Phytoplankton–Zooplankton model is investigated. The results for the existence and uniqueness, and conditions for local stability with topological classifications of the equilibrium solutions are determined. It is also exhibited that at trivial and semitrivial equilibrium solutions, discrete model does not undergo flip bifurcation, but it undergoes Neimark–Sacker bifurcation at interior equilibrium solution under certain conditions. Further, state feedback method is deployed to control the chaos in the under consideration system. The extensive numerical simulations are provided to demonstrate theoretical results.

5 citations


Journal ArticleDOI
TL;DR: In this article , a solution for phytoplankton-toxic phyto-phytoplanka-zooplankton system with q-homotopy analysis transform method (q-HATM) is discussed.
Abstract: The solution for phytoplankton–toxic phytoplankton–zooplankton system with q-homotopy analysis transform method (q-HATM) is discussed. The projected system exemplifies three components (namely, zooplankton, toxic–phytoplankton as well as phytoplankton) and the corresponding nonlinear ordinary differential equations exemplify the zooplankton feeds on phytoplankton. The projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana–Baleanu (AB) operator. The equilibrium points and stability have been discussed with the assistance of the Routh–Hurwitz rule in this work within the frame of generalized calculus. The fixed-point theorem is employed to present the existence and uniqueness of the attained result for the considered model, and we consider five different initial conditions for the projected system. Further, the physical nature of the achieved solution has been captured for fractional order, external force and diverse mass. The achieved consequences explicate that the proposed solution method is highly methodical, easy to implement and accurate to analyze the behavior of the nonlinear system relating to allied areas of science and technology.

4 citations


Journal ArticleDOI
TL;DR: In this article , a system of delay differential equations incorporating prey's refuge, fear, fear-response delay, extra food for predators and their gestation lag is analyzed, and the existence of positive equilibria and the stability of prey-free equilibrium are interrelated.
Abstract: In this paper, we analyze a system of delay differential equations incorporating prey’s refuge, fear, fear-response delay, extra food for predators and their gestation lag. First, we examined the system without delay. The persistence, stability (local and global) and various bifurcations are discussed. We provide detailed analysis for transcritical and Hopf-bifurcation. The existence of positive equilibria and the stability of prey-free equilibrium are interrelated. It is shown that (i) fear can stabilize or destabilize the system, (ii) prey refuge in a specific limit can be advantageous for both species, (iii) at a lower energy level (gained from extra food), the system undergoes a supercritical Hopf-bifurcation and (iv) when the predator gains high energy from extra food, it can survive through a homoclinic bifurcation, and prey may become extinct. The possible occurrence of bi-stability with or without delay is discussed. We observed switching of stability thrice via subcritical Hopf-bifurcation for fear-response delay. On changing some parametric values, the system undergoes a supercritical Hopf-bifurcation for both delay parameters. The delayed system undergoes the Hopf-bifurcation, so we can say that both delay parameters play a vital role in regulating the system’s dynamics. The analytical results obtained are verified with the numerical simulation.

4 citations


Journal ArticleDOI
TL;DR: This research presents a framework for dealing with the issue of diagnosis values presented as “picture fuzzy numbers (PFNs)”, and proposes some new neutral or fair operational laws that incorporate the concept of proportional distribution in order to achieve aneutral or fair remedy to the positive, neutral and negative aspects of PFNs.
Abstract: In Pakistan, a hierarchical healthcare system is an efficient way of addressing the issue of limited and insufficient healthcare services. Identifying the various degrees of disease based on the doctor’s diagnosis is an important step in developing the hierarchical healthcare treatment structure. This research presents a framework for dealing with the issue of diagnosis values presented as “picture fuzzy numbers (PFNs)”. Specifically, the goal of this study is to establish some innovative operational laws and “aggregation operators” (AOs) in a picture fuzzy environment. In this regard, we proposed some new neutral or fair operational laws that incorporate the concept of proportional distribution in order to achieve a neutral or fair remedy to the positive, neutral and negative aspects of PFNs. Based on the developed operational laws, we proposed the “picture fuzzy fairly weighted average operator” and the “picture fuzzy fairly ordered weighted averaging operator”. Compared to previous techniques, the proposed AOs provide more generalized and reliable. Furthermore, using proposed AOs with multiple decision-makers and partial weight information under PFNs, a “multi-criteria decision-making” algorithm is developed. Finally, we provide an example to show how the novel approach can aid hierarchical treatment systems. This is essential for merging the healthcare capabilities of the general public and optimizing the medical care system’s service performance. [ FROM AUTHOR] Copyright of International Journal of Biomathematics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

4 citations


Journal ArticleDOI
TL;DR: In this article , the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied, and numerical analysis and graphical representations are provided to interpret the spread of virus.
Abstract: Considering the prevailing situations, the mathematical modeling and dynamics of novel coronavirus (2019-nCoV) particularly in India are studied in this paper. The goal of this work is to create an effective SEIRS model to study about the epidemic. Four different SEIRS models are considered and solved in this paper using an efficient homotopy perturbation method. A clear picture of disease spreading can be obtained from the solutions derived using this method. We parametrized the model by considering the number of infection cases from 1 April 2020 to 30 June 2020. Finally, numerical analysis and graphical representations are provided to interpret the spread of virus. [ FROM AUTHOR] Copyright of International Journal of Biomathematics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

3 citations


Journal ArticleDOI
TL;DR: In this article , the authors investigated the dynamical behavior of a stochastic SQEIAR epidemic model and established sufficient conditions for extinction of the diseases, and then they derived the necessary conditions for the existence of an ergodic stationary distribution of the positive solutions to the model.
Abstract: In this paper, the dynamical behavior of a stochastic SQEIAR epidemic model is investigated. First of all, we establish sufficient conditions for extinction of the diseases. Then the sufficient conditions for the existence of an ergodic stationary distribution of the positive solutions to the model are obtained by constructing a suitable stochastic Lyapunov function. The existence of stationary distribution implies stochastic weak stability. Furthermore, the optimal control problem is considered to provide a theoretical basis for the prevention and control of the disease. Finally, the theoretical results are verified by numerical simulations.

3 citations


Journal ArticleDOI
TL;DR: In this paper , a delayed mosquito population suppression model, where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function, and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae, is developed and studied.
Abstract: In this paper, a delayed mosquito population suppression model, where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function, and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae, is developed and studied. A threshold value [Formula: see text] for the releases of sterile mosquitoes is determined, and it is proved that the origin is globally asymptotically stable if the number of sterile mosquitoes released is above the threshold value [Formula: see text]. Besides, the case when the number of sterile mosquitoes released stays at a constant level [Formula: see text] is also considered. In the special case, it is also proved that the origin is globally asymptotically stable if and only if [Formula: see text] and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when [Formula: see text]. Numerical examples are also provided to illustrate our main theoretical results.

3 citations


Journal ArticleDOI
TL;DR: The modeling results illustrate that periodical birth and sheep shearing play a significant role in inducing periodical outbreak of brucellosis in Inner Mongolia, and it is exhibited that the annual peak number and the final scale of human bru cellosis cases will be reduced dramatically with the delayed peak time of sheep birth.
Abstract: Brucellosis, a zoonotic disease, has brought about enormous human suffering and tremendous economic burden to animal husbandry in China. However, Inner Mongolia is the hardest hit area of brucellosis in China. A total of 132,037 human cases have been reported from 2010 to 2020. Endogenous mechanisms of brucellosis spreading across Inner Mongolia till remains to be revealed. We propose a periodic epidemic model to investigate the effect of periodic parameter changes on brucellosis epidemics. Then we evaluate the basic reproduction number [Formula: see text] and analyze the global dynamics of the model. Furthermore, key parameters related to periodic transmission are estimated based on the monthly data of human brucellosis cases and the trend of newly infected human brucellosis cases are predicted in Inner Mongolia. Our modeling results illustrate that periodical birth and sheep shearing play a significant role in inducing periodical outbreak of brucellosis in Inner Mongolia. Moreover, it is exhibited that the annual peak number and the final scale of human brucellosis cases will be reduced dramatically with the delayed peak time of sheep birth. While the annual peak time will be lagged and the annual peak number will be decreased as the peak time of sheep shearing is postponed. In addition, we discover that it is difficult to stem brucellosis even if all sheep are vaccinated besides ewes. Nevertheless, the detection rate exceed a certain value 0.032 or the decaying rate of Brucella surpass a critical value 0.585, the human brucellosis can be regulated in Inner Mongolia according to the sensitivity analysis of [Formula: see text]. The insights shed herein may contribute to the careful implementation of brucellosis control strategies in other regions.

3 citations


Journal ArticleDOI
TL;DR: In this article , an optimal treatment strategy for combined antiretroviral drugs, which can maximize healthy CD4 + T cells level with minimum side effects and cost is proposed.
Abstract: This paper mainly targets to deduce an optimal treatment strategy for combined antiretroviral drugs, which can maximize healthy CD4 + T cells level with minimum side effects and cost. For this purpose, we consider a within-host treatment model for the HIV infection with two controls incorporating full logistic proliferation of healthy CD4 + T cells, cure rate and fusion effect. These two controls represent the effects of reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs), respectively. The model analysis begins with proving different basic properties like non-negativity, boundedness of the model solutions and calculation of the basic reproduction number of the model under consideration. Then, stability results are obtained for HIV infection-free equilibrium point and also, a critical efficacy for the combined therapies is calculated. After that, the optimal control problem is proposed and solved numerically using a forward–backward iterative method. Finally, we obtain an optimal treatment strategy that can maximize healthy CD4 + T cells count and control the viral load, and HIV-infected CD4 + T cells count to an undetectable level resulting in improved health conditions of infected individuals.

3 citations


Journal ArticleDOI
TL;DR: In this paper , a stochastic delayed epidemic model with double epidemic hypothesis and vaccination incorporating Lévy noise was investigated and sufficient conditions for extinction and persistence in the mean of the two epidemics were given.
Abstract: In this paper, we investigate a stochastic delayed epidemic model with double epidemic hypothesis and vaccination incorporating Lévy noise. First, we show that this model has a unique global positive solution. Furthermore, we give sufficient conditions for extinction and persistence in the mean of the two epidemics and we prove that the two diseases can coexist under some conditions. Finally, we present some examples to illustrate the analytical results by numerical simulations.

Journal ArticleDOI
TL;DR: In this article , a delayed differential model of citrus Huanglongbing infection is analyzed, in which the latencies of the citrus tree and Asian citrus psyllid are considered as two time delay factors.
Abstract: In this paper, a delayed differential model of citrus Huanglongbing infection is analyzed, in which the latencies of the citrus tree and Asian citrus psyllid are considered as two time delay factors. We compute the equilibrium points and the basic reproductive numbers with and without time delays, i.e. [Formula: see text] and [Formula: see text], and then show that [Formula: see text] completely determines the local stability of the disease-free equilibrium. Moreover, the conditions for the existence of transcritical bifurcation are derived from Sotomayor’s Theorem. The stability of the endemic equilibrium and the existence of Hopf bifurcation are investigated in four cases: (1) [Formula: see text], (2) [Formula: see text], (3) [Formula: see text] and (4) [Formula: see text]. Optimal control theory is then applied to the model to study two time-dependent treatment efforts and minimize the infection in citrus and psyllids, while keeping the implementation cost at a minimum. Numerical simulations of the overall systems are implemented in MatLab for demonstration of the theoretical results.

Journal ArticleDOI
TL;DR: In this paper , a cancer virotherapy model with virus lytic cycle and diffusion term is proposed and the conditions for local stability of the constant equilibria of system are given.
Abstract: In this paper, we propose a cancer virotherapy model with virus lytic cycle and diffusion term. Spatiotemporal dynamic properties of the cancer virotherapy system are studied. First, by analyzing the roots distribution of the characteristic equation and transcendental equation, the conditions for the local stability of the constant equilibria of system are given. Second, we select delay as the bifurcation parameter, the existence conditions of Hopf bifurcation are given. By using the center manifold theory and normal form method of partial functional differential equation, the detailed formulae for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are given. Finally, some numerical simulations are given.

Journal ArticleDOI
TL;DR: In this article , an integrated pest management Filippov model with group defense behavior is established, which takes the population density of pests as the control index of integrated management, and the dynamics of the established model are systematically analyzed, including the sliding mode dynamics, the existence and global stability of the real, virtual and pseudo equilibrium, as well as boundary-node and boundary-focus bifurcation.
Abstract: In this paper, an integrated pest management Filippov model with group defense behavior is established, which takes the population density of pests as the control index of integrated pest management. First, under the condition that both subsystems have a globally asymptotically stable equilibrium, the dynamics of the established model are systematically analyzed, including the sliding mode dynamics, the existence and global stability of the real, virtual and pseudo equilibrium, as well as boundary-node and boundary-focus bifurcation. Next, we study the complex dynamics in the Filippov model when an unstable node (focus) or a stable limit cycle occurs in the subsystem by using numerical simulations. The results show that although there are no closed orbits in subsystem, a stable periodic solution may exist for Filippov system after switching perturbation. Finally, we conclude that the group defense behavior of pest makes it harder to control.

Journal ArticleDOI
TL;DR: In this paper , the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically, and numerically were analyzed.
Abstract: This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically, and numerically. The analytical results are obtained using thenormal form technique and numerical results are obtained using the numerical continuation method. For this model, a number of bifurcations are studied, including the transcritical (pitchfork) and flip bifurcations, the Neimark–Sacker (NS) bifurcations, and the strong resonance bifurcations. We especially determine the dynamical behaviors of the model for higher iterations up to fourth-order. Numerical simulation is employed to present a closed invariant curve emerging about an NS point, and its breaking down to several closed invariant curves and eventuality giving rise to a chaotic strange attractor by increasing the bifurcation parameter.

Journal ArticleDOI
TL;DR: In this article , a mathematical model of hepatitis C Virus (HCV) infection is presented, which is based on non-local fractional order and with non-singular kernel, and the existence and uniqueness of the system is proven and its stability is analyzed.
Abstract: In this paper, we study a mathematical model of Hepatitis C Virus (HCV) infection. We present a compartmental mathematical model involving healthy hepatocytes, infected hepatocytes, non-activated dendritic cells, activated dendritic cells and cytotoxic T lymphocytes. The derivative used is of non-local fractional order and with non-singular kernel. The existence and uniqueness of the system is proven and its stability is analyzed. Then, by applying the Laplace Adomian decomposition method for the fractional derivative, we present the semi-analytical solution of the model. Finally, some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions.

Journal ArticleDOI
TL;DR: In this article , a discrete-time dynamical system generated by a modified susceptible-infected-recovered-dead model (SIRD model; nonlinear operator) in three-dimensional simplex is considered.
Abstract: This paper deals with a discrete-time dynamical system generated by a modified susceptible–infected–recovered–dead model (SIRD model; nonlinear operator) in three-dimensional simplex. We introduce a novel approach that incorporates the SIRD model with the quadratic stochastic operator (QSO) that allows for real-time forecasting. The basic reproductive number [Formula: see text] is obtained. We describe the set of fixed points of the operator and demonstrate that all fixed points are non-hyperbolic. Further, we study the asymptotical behavior of the trajectories of this system and show that SIRD operators have a regularity property.

Journal ArticleDOI
TL;DR: In this article , a discrete evolutionary Beverton-Holt population model is derived using evolutionary game theory methodology and takes into consideration the strong Allee effect related to predation saturation.
Abstract: In this paper, we have derived a discrete evolutionary Beverton–Holt population model. The model is built using evolutionary game theory methodology and takes into consideration the strong Allee effect related to predation saturation. We have discussed the existence of the positive fixed point and examined its asymptotic stability. Analytically, we demonstrated that the derived model exhibits Neimark–Sacker bifurcation when the maximal predator intensity is at lower values. All chaotic behaviors are justified numerically. Finally, to avoid these chaotic features and achieve asymptotic stability, we implement two chaos control methods.

Journal ArticleDOI
TL;DR: In this paper , a mathematical analysis of the global dynamics of a hepatitis C virus infection model in vivo is carried out, and the authors prove that the solutions of the new model with positive initial values are positive, exist globally in time and are bounded.
Abstract: In this paper, a mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both extracellular and intracellular levels of infection. At present, most mathematical modeling of viral kinetics after treatment only addresses the process of infection of a cell by the virus and the release of virions by the cell, while the processes taking place inside the cell are not included. We prove that the solutions of the new model with positive initial values are positive, exist globally in time and are bounded. The model has two virus-free steady states. They are distinguished by the fact that viral RNA is absent inside the cells in the first state and present inside the cells in the second. There are basic reproduction numbers associated to each of these steady states. If the basic reproduction number of the first steady state is less than one, then that state is asymptotically stable. If the basic reproduction number of the first steady state is greater than one and that of the second less than one, then the second steady state is asymptotically stable. If both basic reproduction numbers are greater than one, then we obtain various conclusions which depend on different restrictions on the parameters of the model. Under increasingly strong assumptions, we prove that there is at least one positive steady state (infected equilibrium), that there is a unique positive steady state and that the positive steady state is stable. We also give a condition under which every positive solution converges to a positive steady state. This is proved by methods of Li and Muldowney. Finally, we illustrate the theoretical results by numerical simulations.

Journal ArticleDOI
TL;DR: The findings suggest that in the case of limited medical resources, the high treatment rate and awareness of the population are very helpful to control the disease and the eradication of disease also depends on initial population sizes.
Abstract: The pharmaceutical interventions of emerging infectious diseases are constrained by the available medical resources such as drugs, vaccines, hospital beds, isolation places and the efficiency of the treatment. The awareness of the population also plays an important role in reducing contacts and consequently, reducing the disease transmission rate. In this paper, we propose a multi-group Susceptible, Infected and Recovered (SIR) epidemic model incorporating the awareness of population and the saturated treatment function that describes the effects of the availability of medical resources for treatment. We assume that the treatment of the infected individuals of a group is affected by the medical resources for the treatment of each group. We calculate the basic reproduction number [Formula: see text] in the term of the awareness parameter using the next generation approach. We determine the local and global stabilities of equilibrium (disease free equilibrium and endemic equilibrium) in terms of [Formula: see text] and the availability of medical resources for treatment. We obtain that backward bifurcation occurs at [Formula: see text] along with the existence of multiple endemic equilibria when [Formula: see text] Further, we consider the special case with a single group epidemic system and ensure the existence of multiple endemic equilibria. We showed a necessary condition on the parameter related to the availability of medical resources when backward bifurcation occurs. This situation indicates that reducing the basic reproduction number below unity is not sufficient to remove the disease when the medical resources for treatment are scarce. We used numerical simulations to support and counterpart our theoretical results and discussed the impacts of the awareness of susceptible population and availability of medical resources for treatment in each group, on the epidemic size of each group. Our findings suggest that in the case of limited medical resources, the high treatment rate and awareness of the population are very helpful to control the disease (to reduce the prevalence of infection) and the eradication of disease also depends on initial population sizes. More importantly, it is also obtained that sufficient medical resources for every group are required to eradicate the disease from an entire population.

Journal ArticleDOI
TL;DR: In this article , a mathematical model to analyze the interaction of two viruses, HIV-1 and HTLV-I with the immune system is presented. But, the model is not suitable for the analysis of human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLVI) co-infection.
Abstract: The main target of both human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) is the CD4 + T cell which is considered the key player in the immune system. Moreover, HIV-1 has another target that is the macrophages. The present paper aims to formulate and develop a mathematical model to analyze the interaction of two viruses, HIV-1 and HTLV-I with the immune system. We determine a bounded domain for the concentrations of the model’s compartments. We discuss the dynamical behavior of the model and analyze the existence and stability of the system’s steady states. The global asymptotic stability of all steady states is proven by utilizing the Lyapunov method. We also demonstrate the dynamical behavior of the system numerically. The significant impact of macrophages on the HTLV-I/HIV-1 co-infection dynamics is discussed. Our developed model will contribute to the understanding of HTLV-I/HIV-1 co-infection dynamics and help to choose different treatment strategies against HIV-1 and HTLV-I.

Journal ArticleDOI
TL;DR: In this paper , the bifurcation analysis in a discrete-time Leslie-Gower predator-prey model with constant yield predator harvesting was investigated, and the stability analysis for the fixed points of the discretized model was shown briefly.
Abstract: This work investigates the bifurcation analysis in a discrete-time Leslie–Gower predator–prey model with constant yield predator harvesting. The stability analysis for the fixed points of the discretized model is shown briefly. In this study, the model undergoes codimension-1 bifurcation such as fold bifurcation (limit point), flip bifurcation (period-doubling) and Neimark–Sacker bifurcation at a positive fixed point. Further, the model exhibits codimension-2 bifurcations, including Bogdanov–Takens bifurcation and generalized flip bifurcation at the fixed point. For each bifurcation, by using the critical normal form coefficient method, various critical states are calculated. To validate our analytical findings, the bifurcation curves of fixed points are drawn by using MATCONTM. The system exhibits interesting rich dynamics including limit cycles and chaos. Moreover, it has been shown that the predator harvesting may control the chaos in the system.

Journal ArticleDOI
TL;DR: In this paper , a mathematical model for solid avascular tumor growth with a time delay in regulatory apoptosis is studied, and the existence and uniqueness of a solution to the model are proved.
Abstract: In this paper, a mathematical model for solid avascular tumor growth with a time delay in regulatory apoptosis is studied. In the model, two types of cell apoptoses are considered, one is natural apoptosis and the other is regulatory apoptosis. The process of regulatory apoptosis is delayed compared to the processes of proliferation and natural apoptosis. The existence and uniqueness of a solution to the model are proved. The long-time asymptotic behavior of the solutions is studied. The results show that the dynamical behavior of solutions to this mathematical model is similar to that of the corresponding quasi-stationary problem for some special parameter values. Numerical simulations of some special parameter values are also given to verify our results.

Journal ArticleDOI
TL;DR: In this paper , the authors investigate the dynamics of the treatments of plant diseases via the Atangana-Baleanu derivative in the sense of Caputo (ABC) and study the existence and uniqueness of solutions of curative and preventive treatment fractional model for plant disease.
Abstract: The growth of the world populations number leads to increasing food needs. However, plant diseases can decrease the production and quality of agricultural harvests. Mathematical models are widely used to model and interpret plant diseases, showing viruses’ transmission dynamics and effects. In this paper, we investigate the dynamics of the treatments of plant diseases via the Atangana–Baleanu derivative in the sense of Caputo (ABC). We study the existence and uniqueness of solutions of curative and preventive treatment fractional model for plant disease. By using Lagrange interpolation, we give numerical simulations and investigate the results at various fractional orders under specific parameters. The results show that the increase of the roguing rate for the most infected plant or the decrease of the rate of planting in the infected area will reduce the plant disease transmissions. For balancing the plant production, the decision-makers can plant in other areas in which there are no infected cases.

Journal ArticleDOI
TL;DR: In this article , the authors applied the Z-type control method to an intraguild crop-pest-natural enemy model, assuming that the natural enemy can predate on both crop and pest populations.
Abstract: In this study, the Z-type control method is applied to an intraguild crop-pest-natural enemy model, assuming that the natural enemy can predate on both crop and pest populations. For this purpose, the indirect Z-type controller is considered in the natural enemy population. After providing the design function for the crop-pest-natural enemy model with Z-control, we find the analytical expression of the update parameter. The findings indicate that the uncontrolled system can produce chaos through period-doubling bifurcation due to crop over-consumption by the pest population. We draw a Poincaré map to confirm the occurrence of chaos and compute the maximum Lyapunov exponent. As the observations further indicate that the pest population can be controlled by using an indirect Z-control mechanism in the natural enemy population, we postulate that, if natural enemy abundance can be governed by the update parameter, any desired pest population abundance can be achieved through the proposed Z-type controller, thus controlling the pest. To verify these assertions, extensive numerical simulations are performed to explore the potential for practical application of the proposed Z-type controller.

Journal ArticleDOI
TL;DR: It is found that the self-interactions among solitary waves along with generation of relatively small-scale and unstable wave fields contribute to turbulence.
Abstract: Fluid flow dynamics in nature and its applications including hemodynamics are subjected to periodic velocity modulations. The nonlinear evolution equations are perused to understand such fundamental dynamical challenges in hemodynamics. Assuming cardiovascular hemodynamic system as a finite dissipative system and blood as an incompressible Newtonian fluid, a nonlinear evolution equation for pulsatile blood flow in the aorta during the cardiac cycle is modeled. The main results for generalized [Formula: see text]-dimensional nonlinear evolution equation, using the Lie group of transformations method are introduced. The implications of traveling wave solutions to describe the pulsatile blood flow in the aorta are discussed. It is found that the self-interactions among solitary waves along with generation of relatively small-scale and unstable wave fields contribute to turbulence.

Journal ArticleDOI
TL;DR: In this article , the numerical solution of stochastic FitzHugh-Nagumo equation (SFNE) has been obtained by Chebyshev spectral collocation using semi-implicit Euler-Maruyama scheme.
Abstract: In this paper, the numerical solution of stochastic FitzHugh–Nagumo equation (SFNE) has been obtained by Chebyshev spectral collocation. Semi-implicit Euler–Maruyama scheme has been used for temporal variable to discretize the stochastic FitzHugh–Nagumo equation. A detailed stability analysis for stochastic FitzHugh–Nagumo equation has also been discussed. Graphical representations of obtained results of the stochastic FitzHugh–Nagumo equation have been discussed to provide a clear idea about the behavior of the solutions.

Journal ArticleDOI
TL;DR: In this paper , the authors proposed and analyzed an ecosystem consisting of two types of preys and their predators, and applied Pontryagin's maximum principle to find the optimal control.
Abstract: This paper expresses the concepts, methods, and applications of mathematical models in agriculture. We propose and analyze an ecosystem consisting of two types of preys and their predators; here the prey-I like sugarcane crops that take a long time to grow and prey-II like vegetables, which have a short life, are grown with sugarcane crops and predators that harm both prey-I and prey-II. The various equilibria of the system are obtained, and the stability conditions are analyzed. Furthermore, a comprehensive analysis of the optimal control strategy is also performed. The optimal control model includes the use of three control variables, such as pesticide application rate, biomass application rate, and control of Cassava mosaic virus in the system. Finally, we apply Pontryagin’s maximum principle to find the optimal control. Furthermore, analytical results are verified by numerical simulations.

Journal ArticleDOI
TL;DR: Wang et al. as mentioned in this paper developed a new concise approach to determine the combination coefficients in the Lyapunov function candidate for the model and its time derivative in the case that both are the linear combinations of several Volterra-type functions, which highly simplified the computations in global dynamical analysis for the nonlinear high-dimensional model.
Abstract: This paper formulates a diffusive tuberculosis (TB) model with early and late latent infections, vaccination and treatment that may more properly describe the slow and fast dynamics of TB transmission. We develop a new concise approach to determine the combination coefficients in the Lyapunov function candidate for the model and its time derivative in the case that both are the linear combinations of several Volterra-type functions, which highly simplifies the computations in global dynamical analysis for the nonlinear high-dimensional model. Based on the TB case data reported in China, the parameter values of the model are estimated. We further predict the TB prevalence trend in China. Sensitivity analysis for the control reproduction number and endemic equilibrium is conducted to seek some effective interventions that can significantly reduce initial TB transmission and lower TB prevalence levels in China. In the end, numerical simulations show that the bigger diffusive rates pick up the speeds of convergence to the equilibria of the model.

Journal ArticleDOI
TL;DR: In this article , the influence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior was investigated for a class of Nicholson's blowflies with patch structure and multiple pairs of distinct time varying delays.
Abstract: This paper is intended to investigate a class of Nicholson’s blowflies system with patch structure and multiple pairs of distinct time-varying delays, we are interested in finding the influence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior. By using the theory of functional differential equations, the fluctuation lemma, and the technique of differential inequalities, some new delay-dependent criteria on the global attractivity of the positive equilibrium point are established. In addition, the effectiveness and feasibility of the theoretical achievements are illustrated by some numerical simulations.