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This paper performs a detailed analysis and explores optimal control strategies for a fractional-order SIV epidemic model, incorporating a nonmonotonic incidence rate. In this paper, the population of vaccinated individuals is included in the disease dynamics model. After proving the non-negative boundedness of the fractional-order SIV model, we focus on analyzing the equilibrium point characteristics of the model, delving into its existence, uniqueness, and stability analysis. In addition, our research includes formulating optimal control strategies specifically aimed at minimizing the number of infections while keeping costs as low as possible. To validate the theoretical findings and uncover the practical efficacy and prospects of control measures in mitigating epidemic spread, numerical simulations are performed. [ABSTRACT FROM AUTHOR]

This paper investigates the trends of three different species interacting in the same ecosystem. The study is conducted on the ecosystem which consists of a prey S1 and two predators S2 and S3 in such a way that S2 is a predator of S1 and S3 is a predator of both S1 and S2. In addition, S1 and S2 share the same food which is the main food for S1 and the alternative food for S2. A system of three simultaneous nonlinear partial differential equations is used to represent this situation. The local stability of all constant equilibrium points is discussed after showing their feasibility. In addition, a condition for which a coexisting constant equilibrium point is asymptotically globally stable is also investigated. The results showed that the system has eight constant equilibrium points. Five of them are unstable, while the three remaining are asymptotically locally stable under some conditions on the parameters that are involved in the model. [ABSTRACT FROM AUTHOR]

In a previous paper (Feng et al., J. Differential Equations (2023)), we studied a seasonally interactive model between closed seasons and open seasons with Michaelis-Menten type harvesting, in which we assumed that the harvesting quantity was relatively large (0 < κ = l G c E < 1) and obtained a length threshold of the closed season T ¯ ⁎ depending on the harvesting parameter and the seasonal fluctuation period. It was shown that the origin is globally asymptotically stable if and only if T ¯ ≤ T ¯ ⁎ , and there exists a unique globally asymptotically stable T -periodic solution if and only if T ¯ > T ¯ ⁎. In this paper, we continue to investigate the periodic dynamics of this model when the harvesting quantity is relatively small (κ = l G c E ≥ 1). By finding another smaller length threshold T ¯ ⁎ ∈ (0 , T ¯ ⁎) , we determine the number of periodic solutions and study their stability, which imply the occurrence of bifurcation of periodic solutions. Our results demonstrate that designing the closed harvesting season properly can prevent the species from extinction. Moreover, by comparing with the continuous harvesting model and combining the results in our previous paper and this article, we provide a complete understanding on the global dynamics for the periodic switching model. Some numerical simulations are also carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates both the local and global stability of a system of rational difference equations and its connection to co-balancing numbers. The study delves into the intricate dynamics of mathematical models and their stability properties, emphasizing the broader implications of global stability. Additionally, the investigation extends to the role of co-balancing numbers, elucidating their significance in achieving equilibrium within the solutions of the rational difference equations. The interplay between global stability and co-balancing numbers forms a foundational aspect of the analysis. The findings contribute to a deeper understanding of the mathematical structures underlying dynamic systems and offer insights into the factors influencing their stability and equilibrium. This article serves as a valuable resource for mathematicians, researchers, and scholars interested in the intersection of global stability and co-balancing sequences in the realm of rational difference equations. Moreover, the presented examples and figures consistently demonstrate the global asymptotic stability of the equilibrium point throughout the paper. [ABSTRACT FROM AUTHOR]

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional R0 which is based on the disease-free equilibrium, and a new net reproduction number R0 (E*) based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1 and unstable if R0 > 1. Moreover, the endemic equilibrium is locally asymptotically stable if R0(E*) < 1 < R0. [ABSTRACT FROM AUTHOR]

Contracting cancer typically induces a state of terror among the individuals who are affected. Exploring how chemotherapy and anxiety work together to affect the speed at which cancer cells multiply and the immune system's response model is necessary to come up with ways to stop the spread of cancer. This paper proposes a mathematical model to investigate the impact of psychological scare and chemotherapy on the interaction of cancer and immunity. The proposed model is accurately described. The focus of the model's dynamic analysis is to identify the potential equilibrium locations. According to the analysis, it is possible to establish three equilibrium positions. The stability analysis reveals that all equilibrium points consistently exhibit stability under the defined conditions. The bifurcations occurring at the equilibrium sites are derived. Specifically, we obtained transcritical, pitchfork, and saddle-node bifurcation. Numerical simulations are employed to validate the theoretical study and ascertain the minimum therapy dosage necessary for eradicating cancer in the presence of psychological distress, thereby mitigating harm to patients. Fear could be a significant contributor to the spread of tumors and weakness of immune functionality. [ABSTRACT FROM AUTHOR]

This paper presents a study on a Lotka-Volterra ammensalism model that incorporates the fear effect, which can potentially decrease the birth rate and raise the mortality rate of the species. For the autonomous case, equilibrium points' local and global stability are discussed. For the nonautonomous case, sufficient conditions which ensure the persistence and extinction, and global asymptotic stability of the positive solutions are obtained, respectively. The study has shown that with the increase of the fear effect, the final density of the affected population will decrease, and when the fear effect is large enough, it will cause population's extinction. [ABSTRACT FROM AUTHOR]

The application of mathematical biology and dynamical systems has proven to be an effective approach for studying viral infection models. To contribute to this research, our paper proposes a new CHIKV model that takes into account an adaptive immune response and distributed time delays, which accurately reflects the time lag between initial viral contacts and the production of new active CHIKV particles. By analyzing the model’s qualitative behavior, we establish a biological threshold number that can predict whether CHIKV will be cleared from or persist in the body. We demonstrate the global stability of both CHIKV-present and CHIKV-free steady states using the Lyapunov functional method and LaSalle’s invariance principle. In addition, we conduct numerical simulations to examine how time delays can affect the stability of the steady states. Through these simulations, we gain insights into how varying time delays can influence the persistence or clearance of CHIKV within the host. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the global asymptotic behaviors of a mathematical susceptibleinfected(SI) age-infection-structured human immunodeficiency virus(HIV) model with heterogeneous transmission. Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number R 0. If R 0 < 1, disease-free equilibrium is globally asymptotically stable. If R 0 >1, it shows that diseasefree equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable. The proofs of global stability utilize Lyapunov functions. Besides, the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for R 0 is performed by the method of partial rank correlation coefficient(PRCC). [ABSTRACT FROM AUTHOR]

This paper focuses on the S-asymptotically Periodic oscillation for a type of fractional-order fuzzy Cohen-Grossberg neural networks (CGNNs) by employing some properties of Mittag-Leffler mappings and fixed point theorems. Further, the global asymptotic stability of CGNNs is received. For CGNNs, our works in this paper not only enrich its theoretical achievements, but also expand its application scope. [ABSTRACT FROM AUTHOR]

In this paper, we study the global dynamics of a general reaction-diffusion model based on acid-mediated invasion hypothesis, which is a candidate explanation for the Warburg effect. Our theoretical results characterize the effects of acid resistance and mutual competition of healthy cells and tumor cells on tumor progression in the long term, i.e., whether the healthy cells and tumor cells coexist or the tumor cells prevail after tumor invasion. A key feature of this model is the density-limited tumor diffusion term for tumor cells, which might give rise to the degeneracy of the parabolic equation. To overcome this difficulty, we combine the construction of suitable Lyapunov functionals and upper/lower solutions. This paper continues and improves the work begun in [15]. [ABSTRACT FROM AUTHOR]

This paper considers the dynamical properties of a space and time discrete fractional reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The linear stability of the equilibrium solutions of the considered discrete fractional reaction–diffusion model has been carried out, and a global asymptotic stability analysis has been undertaken. We conducted a global stability analysis using a specialized Lyapunov function that captures the system's historical data, distinguishing it from the integer-order version. This approach significantly advanced our comprehension of the complex stability properties within discrete fractional reaction–diffusion epidemic models. To substantiate the theoretical underpinnings, this paper is accompanied by numerical examples. These examples serve a dual purpose: not only do they validate the theoretical findings, but they also provide illustrations of the practical implications of the proposed discrete fractional system. [ABSTRACT FROM AUTHOR]

In this paper, we present a survey about the latest results in global stability concerning the discrete-time evolutionary Ricker competition model with n species, in both, autonomous and periodic models. The main purpose is to convey some arguments and new ideas concerning the techniques for showing global asymptotic stability of fixed points or periodic cycles in these kind of discrete-time models. In order to achieve this, some open problems and conjectures related to the evolutionary Ricker competition model are presented, which may be a starting point to study global stability, not only in other competition models, but in predator–prey models and Leslie–Gower-type models as well. [ABSTRACT FROM AUTHOR]

In this paper, we consider a food chain model with ratio-dependent functional response and prey-taxis. We first investigate the global existence and boundedness of the unique positive classical solutions of the system in a bounded domain with smooth boundary and Neumann boundary conditions. Then, we analyze the local stability of the system and the existence of Hopf bifurcation. In addition, we prove the global asymptotic stability of steady states under some conditions by constructing a Lyapunov functional, and investigate convergence rates. Finally, we present several numerical simulations to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of population dynamics of an EIS epidemic reaction-diffusion model in spatially heterogeneous environments, where the rates of disease-induced mortality and disease transmission are space dependent. For such a class of systems, we provide clear pictures on the global dynamics in terms of the basic reproduction number R 0 , which improves the local dynamics proposed in Wang and Zhao (2012) [20]. When R 0 ≤ 1 , the disease-free steady state is globally asymptotically stable. Different from earlier works for many epidemic models, we obtain the positive steady states by using bifurcation theory for R 0 > 1 , which can be easily generalized to the case where the reaction-diffusion system involves partial diffusion coefficients of zero. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a two-species competition model with seasonal succession and different harvesting strategies. We aim to comprehend the impact of the proportion of good season on species competition outcomes and harvesting practices. For the case of weak harvest, we establish proportion thresholds for the good season for the species. Based on these threshold settings, we determine conditions for the existence and uniqueness of two semi-trivial periodic solutions and the existence, uniqueness and stability of positive periodic solutions under certain conditions. Numerical simulations and brief discussions are presented to validate our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, the population dynamics of a novel coronavirus are studied. An extended SEIR model with quarantine, hospitalization, and the environment compartment is proposed to simulate the novel coronavirus epidemic. The model considers eight distinct epidemiological classes: susceptible, exposed, asymptomatic, symptomatic, quarantined, hospitalized, recovered, and viruses in the environment. The basic reproduction numbers are determined by using a method called the next-generation matrix. The model has two equilibria: a disease-free equilibrium and an endemic equilibrium. The Lyapunov function and the LaSalle invariance principle are used to analyze the global asymptotical stability of the equilibria of the proposed model. The disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity, and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. To study cost-effectiveness assessments for the four optimum control strategies, we ran numerical simulations. When the four control strategies were compared, it was discovered that Strategy A (public health education and intensive medical treatment) was the most economical and efficient control intervention in the absence of vaccination. However, we observe that strategies A, B, and D are similarly effective at containing COVID-19 in terms of infection prevention. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild- $ N.\,lugens $ N. l u g e n s -eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild $ N.\,lugens $ N. l u g e n s are also given. In addition, the sufficient conditions for the extinction and persistence of the wild $ N.\,lugens $ N. l u g e n s in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild $ N.\,lugens $ N. l u g e n s , and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions. [ABSTRACT FROM AUTHOR]

In this paper we consider the ultimate dynamics of one 4D cancer model which was created for studying the immune response to the two-phenotype tumors. Our approach is based on the localization method of compact invariant sets. The existence of a positively invariant polytope is shown and its size is calculated depending on the parameters of this cancer model. Various convergence conditions to the tumor free equilibrium point were proposed. This property has the biological meaning of global asymptotic tumor eradication (GATE). Further, the case in which local asymptotic tumor eradication (LATE) conditions entail GATE conditions was found. Our theoretical studies of ultimate dynamics are complemented by numerical simulation results. [ABSTRACT FROM AUTHOR]

In this paper, a novel pest-natural enemy model with additional food source and Holling-( p +1) type functional response is put forward for plant pest management by considering multiple food sources for predators. The dynamical properties of the model are investigated, including existence and local asymptotic stability of equilibria, as well as the existence of limit cycles. The inhibition of natural enemy on pest dispersal and the impact of additional food sources on system dynamics are elucidated. In view of the fact that the inhibitory effect of the natural enemy on pest dispersal is slow and in general deviated from the expected target, an integrated pest management model is established by regularly releasing natural enemies and spraying insecticide to improve the control effect. The influence of the control period on the global stability and system persistence of the pest extinction periodic solution is discussed. It is shown that there exists a time threshold, and as long as the control period does not exceed that threshold, pests can be completely eliminated. When the control period exceeds that threshold, the system can bifurcate the supercritical coexistence periodic solution from the pest extinction one. To illustrate the main results and verify the effectiveness of the control method, numerical simulations are implemented in MATLAB programs. This study not only enriched the related content of population dynamics, but also provided certain reference for the management of plant pest. [ABSTRACT FROM AUTHOR]

Reduced population growth at low density has important implications for conservation, colonization success, and wildlife management. In this context, the Allee effect, i.e. the positive relationship between per capita growth rate and biomass of small population density, is a crucial biological phenomenon since it is directly related to population extinction. The present paper deals with a two-species interacting model with a predator–prey relationship, where the prey population experiences the mate-finding Allee effect caused by the predator. We assume that the searching efficiency of prey individuals decreases linearly with predator density due to predation fear and investigate how predation intensity affects predator–prey dynamics. Moreover, we consider the Monod–Haldane type functional response for predator–prey interactions, which shows group defense of prey against the predator. We provide detailed mathematical analyses, including the positivity and boundedness of solutions, all biologically feasible equilibria, and their local and global stabilities. From our detailed mathematical analyses, we observe that when the carrying capacity of prey is low, at most one interior equilibrium exists, and system dynamics is simple compared to the case with high carrying capacity in which multiple coexistence equilibria may exist. We discuss three codimension-one bifurcations mathematically, e.g. Hopf bifurcation, transcritical bifurcation, saddle-node bifurcation. We notice bistability in the system when there are two interior equilibria with high carrying capacity. However, a unique attractor exists when there is only a single interior equilibrium and both populations persist. We perform extensive numerical simulations by varying two parameters simultaneously and explore how the system dynamics become complex when carrying capacity is high compared to low carrying capacity. Moreover, we discuss other important biological phenomena, e.g. the paradox of enrichment, bubbling phenomenon, etc. [ABSTRACT FROM AUTHOR]

In this paper, we establish and study a novel predator–prey model that incorporates: (i) the migration of prey between breeding and non-breeding regions; (ii) the refuge effect of prey; and (iii) the reduction in prey pulse birth rate, in the form of a fear effect, in the presence of predators. Applying the Floquet theory and the comparison theorem of impulsive differential equations, we obtain the sufficient conditions for the stability of the prey-extinction periodic solution and the permanence of the system. Furthermore, we also study the case where the prey population does not migrate. Sufficient conditions for the stability of the prey-extinction periodic solution and the permanence are also established, and the threshold for extinction and permanence of the prey population is obtained. Finally, some numerical simulations are provided to verify the theoretical results. These results provide a theoretical foundation for the conservation of biodiversity. [ABSTRACT FROM AUTHOR]

China bears a heavy burden due to tuberculosis (TB) with hundreds of thousands of people falling ill with the disease every year. Therefore, it is necessary to understand the effectiveness of current control measures in China. In this paper, we first present a TB model that incorporates both vaccination and treatment. Additionally, the model considers TB transmission characteristics such as relapse and variable latency. We then define the basic reproduction number R 0 of the proposed model and indicate that the disease-free equilibrium state is globally asymptotically stable if R 0 < 1 , and the endemic equilibrium state is globally asymptotically stable if R 0 > 1 . We then apply the Grey Wolf Optimizer algorithm to obtain the parameters and initial values of the model by combining TB data collected in China from 2007 to 2020. Through the partial rank correlation coefficient method, we identify the parameters that are most sensitive to R 0 . Based on the analysis results of the model, we propose some suggestions for TB control measures in the conclusion section. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes two mathematical models for the human immunodeficiency virus type-1 (HIV-1) infection with Cytotoxic T Lymphocyte cell (CTL) immune impairment. These models describe the interactions between healthy CD 4 + T cells, latently and actively infected cells, HIV-1 particles, and CTLs. The healthy CD 4 + T cells might be infected when they make contact with: (i) HIV-1 particles due to virus-to-cell (VTC) contact; (ii) latently infected cells due to latent cell-to-cell (CTC) contact; and (iii) actively infected cells due to active CTC contact. Distributed time delays are considered in the second model. We show the nonnegativity and boundedness of the solutions of the systems. Further, we derive basic reproduction numbers ℜ 0 and ℜ ˜ 0 , that determine the existence and stability of equilibria of our proposed systems. We establish the global asymptotic stability of all equilibria by using the Lyapunov method together with LaSalle's invariance principle. We confirm the theoretical results by numerical simulations. The effect of immune impairment, time delay and CTC transmission on the HIV-1 dynamics are discussed. It is found that weak immunity contributes significantly to the development of the disease. Further, we have established that the presence of time delay can significantly decrease the basic reproduction number and then suppress the HIV-1 replication. On the other hand, the presence of latent CTC spread increases the basic reproduction number and then enhances the viral progression. Thus, neglecting the latent CTC spread in the HIV-1 infection model will lead to an underestimation of the basic reproduction number. Consequently, the designed drug therapies will not be accurate or sufficient to eradicate the viruses from the body. These findings may help to improve the understanding of the dynamics of HIV-1 within a host. [ABSTRACT FROM AUTHOR]

Pseudorabies is a highly contagious disease caused by pseudorabies virus (PRV) or suid herpesvirus 1 (SuHV1), causing significant economic losses to the swine industry in countries where the disease exists. In this paper, we formulate an age structure model of pseudorabies virus that takes into account disease-related mortality and vertical transmission. We find a threshold to determine the stability and existence of the disease. We show that there is always a globally asymptotically stable boundary equilibrium if and only if R02 < + q, which means that the disease always exists in piglets and will die out in adult pigs. When R02 >+ q, the boundary equilibrium is unstable and there exists a unique disease-endemic equilibrium, which is globally asymptotically stable. We give detailed proofs of our theoretical results and numerical examples. Brief concluding remarks are also provided. [ABSTRACT FROM AUTHOR]

This paper presents two viral infection models that describe dynamics of the virus under the effect of two distinct types of antibodies. The first model considers the population of five compartments, target cells, infected cells, free virus particles, antibodies type-1 and antibodies type-2. The presence of two types of antibodies can be a result of secondary viral infection. In the second model, we incorporate the latently infected cells. We assume that the antibody responsiveness is given by a combination of the self-regulating antibody response and the predator–prey-like antibody response. For both models, we verify the nonnegativity and boundedness of their solutions, then we outline all possible equilibria and prove the global stability by constructing proper Lyapunov functions. The stability of the uninfected equilibrium EQ 0 and infected equilibrium EQ * is determined by the basic reproduction number R 0 . The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach EQ 0 and EQ * when R 0 ≤ 1 and R 0 > 1 , respectively. We study the sensitivity analysis to show how the values of all the parameters of the suggested model affect R 0 under the given data. The impact of including the self-regulating antibody response and latently infected cells in the viral infection model is discussed. We showed that the presence of the self-regulating antibody response reduces R 0 and makes the system more stabilizable around EQ 0 . Moreover, we established that neglecting the latently infected cells in the viral infection modeling leads to the design of an overflow of antiviral drug therapy. [ABSTRACT FROM AUTHOR]

The oscillatory dynamics of a delayed housefly model is analyzed in this paper. The local and global stabilities at the non-negative equilibria are obtained via analyzing the distribution of eigenvalues and Lyapunov–LaSalle invariance principle, and the model undergoes the supercritical Hopf bifurcation and the transient oscillation. Based on Wu's global Hopf bifurcation theory, the existence of the global bifurcation is established under certain conditions. [ABSTRACT FROM AUTHOR]

The fractional differential equation has a memory property and is suitable for biomathematical modeling. In this paper, a fractional SEQIR epidemic model with saturated incidence and vaccination is constructed. Firstly, for the deterministic fractional system, the threshold conditions for the local and global asymptotic stability of the equilibrium point are obtained by using the stability theory of the fractional differential equation. If R 0 < 1 , the disease-free equilibrium is asymptotically stable, and the disease is extinct; when R 0 > 1 , the endemic equilibrium is asymptotically stable and the disease persists. Secondly, for the stochastic system of integer order, the stochastic stability near the positive equilibrium point is discussed. The results show that if the intensity of environmental noise is small enough, the system is stochastic stable, and the disease will persist. Thirdly, the control variables are coupled into the fractional differential equation to obtain the fractional control system, the objective function is constructed, and the optimal control solution is obtained by using the maximum principle. Finally, the correctness of the theoretical derivation is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as a model of the chlorite iodide malonic acid (CIMA) chemical reaction. With the help of the second order difference operator, we describe the fractional discrete model. Furthermore, using the linearization approach, we established acceptable requirements for the local asymptotic stability of the system's unique equilibrium. Moreover, we employ a Lyapunov functional to show that when the iodide feeding rate is moderate, the constant equilibrium solution is globally asymptotically stable. Finally, numerical models are presented to validate the theoretical conclusions and demonstrate the impact of discretization and fractional-order on system dynamics. The continuous version of the fractional-order Lengyel–Epstein reaction–diffusion system is compared to the discrete-time system under consideration. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a seasonally interactive model between closed seasons and open seasons with Michaelis-Menten type harvesting based on some management and capture methods of renewable resources. It is assumed that the population growth obeys the logistic equation in closed seasons and is captured following Michaelis-Menten type response function in open seasons. We define a length threshold of the closed season T ¯ ⁎ , which depends on the harvesting parameter. Under the extinct condition of the corresponding continuous harvesting model, by setting the closed season, theoretical results show that the origin is globally asymptotically stable if and only if T ¯ ≤ T ¯ ⁎ , and there exists a unique globally asymptotically stable T -periodic solution if and only if T ¯ > T ¯ ⁎. In particular, under the critical conditions on special harvest parameters, it is found that the T -periodic solution still exists as long as an arbitrary positive close season is formulated. Numerical examples are carried out to confirm the obtained theoretical results. Brief conclusions and discussions on our findings are also provided. [ABSTRACT FROM AUTHOR]

The stability of traveling waves for the Lotka–Volterra competition system with three species is investigated in this paper. Specifically, we first show the asymptotic behavior of traveling wave solutions and then establish the local stability and the global stability under the weighted functional space. For local stability, the spectrum approach is used, while for global stability, the comparison principle and squeezing theorem are combined. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new fractional order SIS (frSIS) model by way of continuous time random walk. The value of this study lies in two aspects. Mathematically, we provide a framework for the global stability of the frSIS model, and prove that the basic reproduction number R 0 can be used to govern the dynamics of the frSIS model. If R 0 < 1 , the disease-free equilibrium of the model is globally asymptotically stable; if R 0 > 1 , the endemic equilibrium of the model is globally asymptotically stable. And epidemiologically, we find that, in order to control the spread of the disease, we must decrease the death rate and the average infectious period to make the disease go to extinction, which can provide us with some useful control strategies to regulate disease dynamics. • We established a fractional order SIS model by way of continuous time random walk. • We prove that the basic reproduction number can be used to govern the dynamics of the model. • We provide a framework for proving the global stability of the model. • In order to control the spread of the disease, we must decrease the death rate and average infectious period. [ABSTRACT FROM AUTHOR]

The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value ( R 0 m ) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If R 0 m < 1 , the disease-free equilibrium of the illness is globally asymptotically stable in probability one. If R 0 m > 1 , the disease is permanent in the mean with probability one and has an endemic stationary distribution. Numerical simulations are given to illustrate the theoretical results. Interestingly, we discovered that random fluctuations can suppress outbreaks and control the disease. [ABSTRACT FROM AUTHOR]

In several publications, the dynamical system of HIV and HTLV mono-infections taking into account diffusion, as well as latently infected cells in cellular transmission has been mathematically analyzed. However, no work has been conducted on HTLV/HIV co-infection dynamics taking both factors into consideration. In this paper, a partial differential equations (PDEs) model of HTLV/HIV dual infection was developed and analyzed, considering the cells' and viruses' spatial mobility. CD 4 + T cells are the primary target of both HTLV and HIV. For HIV, there are three routes of transmission: free-to-cell (FTC), latent infected-to-cell (ITC), and active ITC. In contrast, HTLV transmits horizontally through ITC contact and vertically through the mitosis of active HTLV-infected cells. In the beginning, the well-posedness of the model was investigated by proving the existence of global solutions and the boundedness. Eight threshold parameters that determine the existence and stability of the eight equilibria of the model were obtained. Lyapunov functions together with the Lyapunov–LaSalle asymptotic stability theorem were used to investigate the global stability of all equilibria. Finally, the theoretical results were verified utilizing numerical simulations. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID-19) is a respiratory disease that appeared in 2019 caused by a virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). COVID-19 is still spreading and causing deaths around the world. There is a real concern of SARS-CoV-2 coinfection with other infectious diseases. Tuberculosis (TB) is a bacterial disease caused by Mycobacterium tuberculosis (Mtb). SARS-CoV-2 coinfection with TB has been recorded in many countries. It has been suggested that the coinfection is associated with severe disease and death. Mathematical modeling is an effective tool that can help understand the dynamics of coinfection between new diseases and well-known diseases. In this paper, we develop an in-host TB and SARS-CoV-2 coinfection model with cytotoxic T lymphocytes (CTLs). The model investigates the interactions between healthy epithelial cells (ECs), latent Mtb-infected ECs, active Mtb-infected ECs, SARS-CoV-2-infected ECs, free Mtb, free SARS-CoV-2, and CTLs. The model's solutions are proved to be nonnegative and bounded. All equilibria with their existence conditions are calculated. Proper Lyapunov functions are selected to examine the global stability of equilibria. Numerical simulations are implemented to verify the theoretical results. It is found that the model has six equilibrium points. These points reflect two states: the mono-infection state where SARS-CoV-2 or TB occurs as a single infection, and the coinfection state where the two infections occur simultaneously. The parameters that control the movement between these states should be tested in order to develop better treatments for TB and COVID-19 coinfected patients. Lymphopenia increases the concentration of SARS-CoV-2 particles and thus can worsen the health status of the coinfected patient. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune cells. We obtained an immunity-inactivated reproduction number R 0 and an immunity-activated reproduction number R 1 . By analyzing the distributions of roots of the corresponding characteristic equations, the local stability results of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium were obtained. Moreover, by constructing suitable Lyapunov functionals and combining LaSalle's invariance principle and Barbalat's lemma, some sufficient conditions for the global stability of the three types of equilibria were obtained. It was found that the infection-free equilibrium is globally asymptotically stable if R 0 ≤ 1 and unstable if R 0 > 1 ; the immunity-inactivated equilibrium is locally asymptotically stable if R 0 > 1 > R 1 and globally asymptotically stable if R 0 > 1 > R 1 and condition (H1) holds, but unstable if R 1 > 1 ; and the immunity-activated equilibrium is locally asymptotically stable if R 1 > 1 and is globally asymptotically stable if R 1 > 1 and condition (H1) holds. [ABSTRACT FROM AUTHOR]

Co-infections with respiratory viruses were reported in hospitalized patients in several cases. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and influenza A virus (IAV) are two respiratory viruses and are similar in terms of their seasonal occurrence, clinical manifestations, transmission routes, and related immune responses. SARS-CoV-2 is the cause of coronavirus disease 2019 (COVID-19). In this paper, we study the dynamic behaviors of an influenza and COVID-19 co-infection model in vivo. The role of humoral (antibody) immunity in controlling the co-infection is modeled. The model considers the interactions among uninfected epithelial cells (ECs), SARS-CoV-2-infected ECs, IAV-infected ECs, SARS-CoV-2 particles, IAV particles, SARS-CoV-2 antibodies, and IAV antibodies. The model is given by a system of delayed ordinary differential equations (DODEs), which include four time delays: (i) a delay in the SARS-CoV-2 infection of ECs, (ii) a delay in the IAV infection of ECs, (iii) a maturation delay of newly released SARS-CoV-2 virions, and (iv) a maturation delay of newly released IAV virions. We establish the non-negativity and boundedness of the solutions. We examine the existence and stability of all equilibria. The Lyapunov method is used to prove the global stability of all equilibria. The theoretical results are supported by performing numerical simulations. We discuss the effects of antiviral drugs and time delays on the dynamics of influenza and COVID-19 co-infection. It is noted that increasing the delay length has a similar influence to that of antiviral therapies in eradicating co-infection from the body. [ABSTRACT FROM AUTHOR]

The excessive emission of greenhouse gases leads to abnormal climate change. Under this background, China puts forward the dual carbon target. In this paper, we use the analytic hierarchy process to determine the important influencing factor of carbon emissions. Next, we establish a delayed differential equation model of carbon emission-absorption under the influence of China's urbanization. We analyze the existence and stability of the positive equilibrium. Finally, we determine the ranges of parameters and study the impact of urbanization on China's dual carbon target through numerical simulations. The numerical simulation also shows that the system may have globally asymptotically stable equilibrium. Through the simulation results, we conclude whether the dual carbon target of China can be achieved by the scheduled time and give some suggestions that could be taken to achieve this target. The projected results provide some guidance for policy adjustments and also have practical significance in protecting the ecological environment. [ABSTRACT FROM AUTHOR]

This paper presents a testing and numerical modeling program on the global stability and resistance of stainless steel hot-rolled channel section beam–columns under combined compression and minor-axis bending. The testing program comprised material tests, imperfection measurements, and 18 beam–column tests. Following the testing program, systematic numerical simulations were conducted; finite-element models were developed to simulate the test observations and conduct parametric studies to obtain more numerical data. The obtained experimental and numerical results were analyzed and used to perform a design analysis, in which the accuracy of interaction curves prescribed in the US and European design codes for stainless steel hot-rolled channel section beam–columns was assessed comprehensively. The results of the design analysis generally revealed that both the US and European interaction curves yield unduly inaccurate and scattered resistance predictions due to the use of inappropriate curve shape and inaccurate end points. A new design interaction formula is proposed using a more appropriate curve shape and more-accurate end points. The new interaction curve was shown to be capable of offering greatly improved design accuracy and consistency compared with the US and European curves. [ABSTRACT FROM AUTHOR]

In this paper the Multicompartment epidemiological model assumes that. given a contagious illness. a population can be partitioned into individuals that are susceptible to the illness. infected by the illness, and recovered from the illness.S(t) Number of individuals at time t susceptible to the illness;/(thi= 1.2.3.4 Number of individuals at time t infected with the illness.Rs(t) Total number of survivors of the illness at time t. RD(t) Total number of deaths due to the illness at time t. The stability of a disease-free status equilibrium and the existence of endemic equilibrium can be determined by the ratio called the basic reproductive number. Laplace-adomian decomposition method is used to compute an analytical solution of the model study. This paper study the equilibrium. local. global stability under certain conditions. [ABSTRACT FROM AUTHOR]

We study a two-species competition-diffusion-advection system with general intrinsic growth rates and carrying capacities in heterogeneous closed environments, where the two aquatic species have different advection and/or diffusion rates. Some special cases have been widely investigated, for example: the non-advective case [8,9] , the homogeneous case [23,24,40] , the proportional case [20,25]. However, due to the difficulty caused by the diffusion-advection type operators as well as the heterogeneous environments, the approaches developed in the previous papers cannot be directly applied to the general case here. With some new techniques, we characterize the linear stability of the two semi-trivial steady states and establish the non-existence of co-existence steady states in several scenarios. Based on these preparations and the theory of monotone dynamical systems, we establish the main results. Our results indicate that both competitive exclusion and coexistence may occur. Specially, we show a new way for coexistence of two species. [ABSTRACT FROM AUTHOR]

In this paper, we propose a mathematical model for the spread of HIV disease within two different age classes. We define a basic reproduction number R0 that depends on the characteristics of the two age classes. We prove that if R0 < 1, then the disease is extinct in both age classes. In contrast, we prove that if R0 > 1, then the disease is endemic in both age classes. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to formulate two new mathematical models to describe the co-dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and human T-cell lymphotropic virus type-I (HTLV-I) in a host. The models characterizes the interplaying between seven compartments, uninfected ECs, latently SARS-CoV-2-infected ECs, actively SARS-CoV-2-infected ECs, free SARS-CoV-2 particles, uninfected CD4 + T cells, latently HTLV-I-infected CD4 + T cells and actively HTLV-I-infected CD4 + T cells. The models incorporate five intracellular time delays: (i) two delays in the formation of latently SARS-CoV-2-infected ECs and latently HTLV-I-infected CD4 + T cells, (ii) two delays in the reactivation of latently SARS-CoV-2-infected ECs and latently HTLV-I-infected CD4 + T cells, and (iii) maturation delay of new SARS-CoV-2 virions. We consider discrete-time delays and distributed-time delays in the first and second models, respectively. We first investigate the properties of the model's solutions, then we calculate all equilibria and study their global stability. The global asymptotic stability is examined by constructing Lyapunov functionals. The analytical findings are supported via numerical simulation. The impact of time delays on the coinfection progression is discussed. We found that, increasing time delays values can have an antiviral treatment-like impact. Our developed coinfection model can contribute to understand the SARS-CoV-2 and HTLV-I co-dynamics and help to select suitable treatment strategies for COVID-19 patients with HTLV-I. [ABSTRACT FROM AUTHOR]

This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use it to investigate the existence and stability of equilibria. In this regard, we prove that the model undergoes a backward bifurcation phenomenon. We highlight the detrimental impact of aerosol dust by showing that its inhalation augments the reproduction number and enhances the endemic level of NmA.We also highlight the favorable role of vaccine in eliminating the disease when it has a high level of efficacy and is used to protect a large proportion of the population. The theoretical results are supported and illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a reaction-diffusion SIR epidemic model via environmental driven infection in heterogeneous space is proposed. To reflect the prevention and control measures of disease in allusion to the susceptible in the model, the nonlinear incidence function E f (S) is applied to describe the protective measures of susceptible. In the general spatially heterogeneous case of the model, the well-posedness of solutions is obtained. The basic reproduction number R 0 is calculated. When R 0 ≤ 1 the global asymptotical stability of the disease-free equilibrium is obtained, while when R 0 > 1 the model is uniformly persistent. Furthermore, in the spatially homogeneous case of the model, when R 0 > 1 the global asymptotic stability of the endemic equilibrium is obtained. Lastly, the numerical examples are enrolled to verify the open problems. [ABSTRACT FROM AUTHOR]

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a new virus which infects the respiratory system and causes the coronavirus disease 2019 (COVID-19). The coinfection between malaria and COVID-19 has been registered in many countries. This has risen an urgent need to understand the dynamics of coinfection. In this paper, we construct a reaction–diffusion in-host malaria/COVID-19 model. The model includes seven-dimensional partial differential equations that explore the interactions between seven compartments, healthy red blood cells (RBCs), infected RBCs, free merozoites, healthy epithelial cells (ECs), infected ECs, free SARS-CoV-2 particles, and antibodies. The biological validation of the model is confirmed by establishing the nonnegativity and boundedness of the model's solutions. All equilibrium points with the corresponding existence conditions are calculated. The global stability of all equilibria is proved by picking up appropriate Lyapunov functionals. Numerical simulations are used to enhance and visualize the theoretical results. We found that the equilibrium points show the different cases when malaria and SARS-CoV-2 infections occur as mono-infection or coinfection. The shared antibody immune response decreases the concentrations of SARS-CoV-2 and malaria merozoites. This can have an important role in reducing the severity of SARS-CoV-2 if the immune response works effectively. [ABSTRACT FROM AUTHOR]

Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the dynamics of IAV/SARS-CoV-2 coinfection within the host. The influence of SARS-CoV-2-specific and IAV-specific antibody immunities is incorporated. The model simulates the interaction between seven compartments, uninfected epithelial cells, SARS-CoV-2-infected cells, IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria and investigate the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. We perform numerical simulations and demonstrate that they are in good agreement with the theoretical results. The importance of including the antibody immunity into the coinfection dynamics model is discussed. We have found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence is not observed. Finally, we discuss the influence of IAV infection on the dynamics of SARS-CoV-2 single-infection and vice versa. [ABSTRACT FROM AUTHOR]

Social insect colonies' robust and efficient collective behaviors without any central control contribute greatly to their ecological success. Colony migration is a leading subject for studying collective decision-making in migration. In this paper, a general colony migration model with Hill functions in recruitment is proposed to investigate the underlying decision making mechanism and the related dynamical behaviors. Our analysis provides the existence and stability of equilibrium, and the global dynamical behavior of the system. To understand how piecewise functions and Hill functions in recruitment impact colony migration dynamics, the comparisons are performed in both analytic results and bifurcation analysis. Our theoretical results show that the dynamics of the migration system with Hill functions in recruitment differs from that of the migration system with piecewise functions in the following three aspects: (1) all population components in our colony migration model with Hill functions in recruitment are persistent; (2) the colony migration model with Hill functions in recruitment has saddle and saddle-node bifurcations, while the migration system with piecewise functions does not; (3) the system with Hill functions has only equilibrium dynamics, i.e. either has a global stability at one interior equilibrium or has bistablity among two locally stable interior equilibria. Bifurcation analysis shows that the geometrical shape of the Hill functions greatly impacts the dynamics: (1) the system with flatter Hill functions is less likely to exhibit bistability; (2) the system with steeper functions is prone to exhibit bistability, and the steady state of total active workers is closer to that of active workers in the system with piecewise function. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an SVEIR epidemic model with reaction–diffusion and nonlinear incidence. We establish the well-posedness of the solutions and the basic reproduction number R 0 . Moreover, we show that the disease-free steady state is globally asymptotically stable when R 0 < 1 , whereas the disease will be persistent when R 0 > 1 . Furthermore, using the method of Lyapunov functional, we prove the global stability of the positive steady state for the spatial homogeneous model. [ABSTRACT FROM AUTHOR]