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Meetei MZ, DarAssi MH, Altaf Khan M, Koam ANA, Alzahrani E, Ali H. Ahmadini A. Analysis and simulation study of the HIV/AIDS model using the real cases. PLoS One 2024; 19:e0304735. [PMID: 38917173 PMCID: PMC11198809 DOI: 10.1371/journal.pone.0304735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2023] [Accepted: 05/16/2024] [Indexed: 06/27/2024] Open
Abstract
We construct a model to investigate HIV/AIDS dynamics in real cases and study its mathematical analysis. The study examines the qualitative outcomes and confirms the local and global asymptotic stability of both the endemic equilibrium and the disease-free equilibrium. The model's criteria for exhibiting both local and global asymptotically stable behavior are examined. We compute the endemic equilibria and obtain the existence of a unique positive endemic equilibrium. The data is fitted to the model using the idea of nonlinear least-squares fitting. Accurate parameter values are achieved by fitting the data to the model using a 95% confidence interval. The basic reproduction number is computed using parameters that have been fitted or estimated. Sensitivity analysis is performed to discover the influential parameters that impact the reproduction number and the eradication of the disease. The results show that implementing preventive measures can reduce HIV/AIDS cases.
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Affiliation(s)
- Mutum Zico Meetei
- Department of Mathematics, College of Science, Jazan University, Jazan, Kingdom of Saudi Arabia
| | - Mahmoud H. DarAssi
- Department of Basic Sciences, Princess Sumaya University for Technology, Amman, Jordan
| | - Muhammad Altaf Khan
- Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa
| | - Ali N. A. Koam
- Department of Mathematics, College of Science, Jazan University, Jazan, Kingdom of Saudi Arabia
| | - Ebraheem Alzahrani
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
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Aldila D, Dhanendra RP, Khoshnaw SHA, Wijayanti Puspita J, Kamalia PZ, Shahzad M. Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis. Front Public Health 2024; 12:1324858. [PMID: 38665242 PMCID: PMC11043473 DOI: 10.3389/fpubh.2024.1324858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 03/14/2024] [Indexed: 04/28/2024] Open
Abstract
In this article, we present a mathematical model for human immunodeficiency virus (HIV)/Acquired immune deficiency syndrome (AIDS), taking into account the number of CD4+T cells and antiretroviral treatment. This model is developed based on the susceptible, infected, treated, AIDS (SITA) framework, wherein the infected and treated compartments are divided based on the number of CD4+T cells. Additionally, we consider the possibility of treatment failure, which can exacerbate the condition of the treated individual. Initially, we analyze a simplified HIV/AIDS model without differentiation between the infected and treated classes. Our findings reveal that the global stability of the HIV/AIDS-free equilibrium point is contingent upon the basic reproduction number being less than one. Furthermore, a bifurcation analysis demonstrates that our simplified model consistently exhibits a transcritical bifurcation at a reproduction number equal to one. In the complete model, we elucidate how the control reproduction number determines the stability of the HIV/AIDS-free equilibrium point. To align our model with the empirical data, we estimate its parameters using prevalence data from the top four countries affected by HIV/AIDS, namely, Eswatini, Lesotho, Botswana, and South Africa. We employ numerical simulations and conduct elasticity and sensitivity analyses to examine how our model parameters influence the control reproduction number and the dynamics of each model compartment. Our findings reveal that each country displays distinct sensitivities to the model parameters, implying the need for tailored strategies depending on the target country. Autonomous simulations highlight the potential of case detection and condom use in reducing HIV/AIDS prevalence. Furthermore, we identify that the quality of condoms plays a crucial role: with higher quality condoms, a smaller proportion of infected individuals need to use them for the potential eradication of HIV/AIDS from the population. In our optimal control simulations, we assess population behavior when control interventions are treated as time-dependent variables. Our analysis demonstrates that a combination of condom use and case detection, as time-dependent variables, can significantly curtail the spread of HIV while maintaining an optimal cost of intervention. Moreover, our cost-effectiveness analysis indicates that the condom use intervention alone emerges as the most cost-effective strategy, followed by a combination of case detection and condom use, and finally, case detection as a standalone strategy.
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Affiliation(s)
- Dipo Aldila
- Department of Mathematics, Universitas Indonesia, Depok, Indonesia
| | | | | | | | | | - Muhammad Shahzad
- Department of Mathematics and Statistics, The University of Haripur, Haripur, KP, Pakistan
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Li W, Cai S, Zhai X, Ou J, Zheng K, Wei F, Mao X. Transmission dynamics of symptom-dependent HIV/AIDS models. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:1819-1843. [PMID: 38454662 DOI: 10.3934/mbe.2024079] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/09/2024]
Abstract
In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0^s $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.
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Affiliation(s)
- Wenshuang Li
- School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
| | - Shaojian Cai
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Xuanpei Zhai
- School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China
| | - Jianming Ou
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Kuicheng Zheng
- Fujian Provincial Center for Disease Control and Prevention, Fuzhou 350012, China
| | - Fengying Wei
- School of Mathematics and Statistics, Fuzhou University, Fuzhou 350116, Fujian, China
- Center for Applied Mathematics of Fujian Province, Fuzhou University, Fuzhou 350116, Fujian, China
- Key Laboratory of Operations Research and Control of Universities in Fujian, Fuzhou University, Fuzhou 350116, Fujian, China
| | - Xuerong Mao
- Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
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A Higher-Order Galerkin Time Discretization and Numerical Comparisons for Two Models of HIV Infection. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2022; 2022:3599827. [DOI: 10.1155/2022/3599827] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Revised: 09/10/2022] [Accepted: 09/20/2022] [Indexed: 11/11/2022]
Abstract
Human immunodeficiency virus (HIV) infection affects the immune system, particularly white blood cells known as CD4+ T-cells. HIV destroys CD4+ T-cells and significantly reduces a human’s resistance to viral infectious diseases as well as severe bacterial infections, which can lead to certain illnesses. The HIV framework is defined as a system of nonlinear first-order ordinary differential equations, and the innovative Galerkin technique is used to approximate the solutions of the model. To validate the findings, solve the model employing the Runge-Kutta (RK) technique of order four. The findings of the suggested techniques are compared with the results obtained from conventional schemes such as MuHPM, MVIM, and HPM that exist in the literature. Furthermore, the simulations are performed with different time step sizes, and the accuracy is measured at various time intervals. The numerical computations clearly demonstrate that the Galerkin scheme, in contrast to the Runge-Kutta scheme, provides incredibly precise solutions at relatively large time step sizes. A comparison of the solutions reveals that the obtained results through the Galerkin scheme are in fairly good agreement with the RK4 scheme in a given time interval as compared to other conventional schemes. Moreover, having performed various numerical tests for assessing the efficiency and computational cost (in terms of time) of the suggested schemes, it is observed that the Galerkin scheme is noticeably slower than the Runge-Kutta scheme. On the other hand, this work is also concerned with the path tracking and damped oscillatory behaviour of the model with a variable supply rate for the generation of new CD4+ T-cells (based on viral load concentration) and the HIV infection incidence rate. Additionally, we investigate the influence of various physical characteristics by varying their values and analysing them using graphs. The investigations indicate that the lateral system ensured more accurate predictions than the previous model.
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Gupta RK, Pal S, Misra AK. Modeling the impact of precautionary measures and sanitation practices broadcasted through media on the dynamics of bacterial diseases. MODELING EARTH SYSTEMS AND ENVIRONMENT 2022; 9:397-412. [PMID: 36059593 PMCID: PMC9420191 DOI: 10.1007/s40808-022-01469-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 07/13/2022] [Indexed: 06/15/2023]
Abstract
The media has a significant contribution in spreading awareness by broadcasting various programs about prevalent diseases in the society along with the role of providing information, feeding news and educating a large mass. In this paper, the effect of media programs promoting precautionary measures and sanitation practices to control the bacterial infection in the community is modeled and analyzed considering the number of media programs as a dynamical variable. In the modeling phenomena, human population is partitioned into three classes; susceptible, infected and recovered. The disease is supposed to spread by direct contact of susceptible with infected individuals and indirectly by the ingestion of bacteria present in the environment. The growth in the media programs is considered proportional to the size of infected population and the impact of these programs on the indirect disease transmission rate and bacteria shedding rate by infected individuals is also considered. The feasibility of equilibria and their stability conditions are obtained. Model analysis reveals that broadcasting media programs and increasing its effectiveness shrink the size of infected class and control the spread of disease to a large extent.
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Affiliation(s)
- Rabindra Kumar Gupta
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221 005 India
- Department of Mathematics, Butwal Multiple Campus, T.U., Butwal, Lumbini 284403 Nepal
| | - Soumitra Pal
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221 005 India
| | - A. K. Misra
- Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, 221 005 India
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Cui X, Xue D, Li T. Fractional-order delayed Ross-Macdonald model for malaria transmission. NONLINEAR DYNAMICS 2022; 107:3155-3173. [PMID: 35095196 PMCID: PMC8782717 DOI: 10.1007/s11071-021-07114-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 11/28/2021] [Indexed: 06/14/2023]
Abstract
This paper proposes a novel fractional-order delayed Ross-Macdonald model for malaria transmission. This paper aims to systematically investigate the effect of both the incubation periods of Plasmodium and the order on the dynamic behavior of diseases. Utilizing inequality techniques, contraction mapping theory, fractional linear stability theorem, and bifurcation theory, several sufficient conditions for the existence and uniqueness of solutions, the local stability of the positive equilibrium point, and the existence of fractional-order Hopf bifurcation are obtained under different time delays cases. The results show that time delay can change the stability of system. System becomes unstable and generates a Hopf bifurcation when the delay increases to a certain value. Besides, the value of order influences the stability interval size. Thus, incubation periods and the order have a major effect on the dynamic behavior of the model. The effectiveness of the theoretical results is shown through numerical simulations.
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Affiliation(s)
- Xinshu Cui
- College of Information Science and Engineering, Northeastern University, Shenyang, 110819 Liaoning China
| | - Dingyu Xue
- College of Information Science and Engineering, Northeastern University, Shenyang, 110819 Liaoning China
| | - Tingxue Li
- College of Information Science and Engineering, Northeastern University, Shenyang, 110819 Liaoning China
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Caputo fractional-order SEIRP model for COVID-19 Pandemic. ALEXANDRIA ENGINEERING JOURNAL 2022; 61:829-845. [PMCID: PMC8096164 DOI: 10.1016/j.aej.2021.04.097] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 04/25/2021] [Accepted: 04/27/2021] [Indexed: 06/15/2023]
Abstract
We propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19 pandemic. The newly proposed nonlinear fractional order model is an extension of a recently formulated integer-order COVID-19 mathematical model. Using basic concepts such as continuity and Banach fixed-point theorem, existence and uniqueness of the solution to the proposed model were shown. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers and generalized Ulam-Hyers stability criteria. The concept of next-generation matrix was used to compute the basic reproduction number R0, a number that determines the spread or otherwise of the disease into the general population. We also investigated the local asymptotic stability for the derived disease-free equilibrium point. Numerical simulation of the constructed epidemic model was carried out using the fractional Adam-Bashforth-Moulton method to validate the obtained theoretical results.
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Chukwu CW, Nyabadza F, Fatmawati F. Modelling the potential role of media campaigns on the control of Listeriosis. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:7580-7601. [PMID: 34814264 DOI: 10.3934/mbe.2021375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Human Listeria infection is a food-borne disease caused by the consumption of contaminated food products by the bacterial pathogen, Listeria. In this paper, we propose a mathematical model to analyze the impact of media campaigns on the spread and control of Listeriosis. The model exhibited three equilibria namely; disease-free, Listeria-free and endemic equilibria. The food contamination threshold is determined and the local stability analyses of the model is discussed. Sensitivity analysis is done to determine the model parameters that most affect the severity of the disease. Numerical simulations were carried out to assess the role of media campaigns on the Listeriosis spread. The results show that; an increase in the intensity of the media awareness campaigns, the removal rate of contaminated food products, a decrease in the contact rate of Listeria by humans results in fewer humans getting infected, thus leading to the disease eradication. An increase in the depletion of media awareness campaigns results in more humans being infected with Listeriosis. These findings may significantly impact policy and decision-making in the control of Listeriosis disease.
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Affiliation(s)
- C W Chukwu
- Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park Kingsway Campus, Johannesburg P. O. Box 524, 2006, South Africa
- Postdoc Fellow Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia
| | - F Nyabadza
- Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park Kingsway Campus, Johannesburg P. O. Box 524, 2006, South Africa
| | - Fatmawati Fatmawati
- Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga, Surabaya 60115, Indonesia
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Moussa YEH, Boudaoui A, Ullah S, Bozkurt F, Abdeljawad T, Alqudah MA. Stability analysis and simulation of the novel Corornavirus mathematical model via the Caputo fractional-order derivative: A case study of Algeria. RESULTS IN PHYSICS 2021; 26:104324. [PMID: 34055583 PMCID: PMC8141347 DOI: 10.1016/j.rinp.2021.104324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Revised: 05/09/2021] [Accepted: 05/10/2021] [Indexed: 05/04/2023]
Abstract
The novel coronavirus infectious disease (or COVID-19) almost spread widely around the world and causes a huge panic in the human population. To explore the complex dynamics of this novel infection, several mathematical epidemic models have been adopted and simulated using the statistical data of COVID-19 in various regions. In this paper, we present a new nonlinear fractional order model in the Caputo sense to analyze and simulate the dynamics of this viral disease with a case study of Algeria. Initially, after the model formulation, we utilize the well-known least square approach to estimate the model parameters from the reported COVID-19 cases in Algeria for a selected period of time. We perform the existence and uniqueness of the model solution which are proved via the Picard-Lindelöf method. We further compute the basic reproduction numbers and equilibrium points, then we explore the local and global stability of both the disease-free equilibrium point and the endemic equilibrium point. Finally, numerical results and graphical simulation are given to demonstrate the impact of various model parameters and fractional order on the disease dynamics and control.
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Affiliation(s)
| | - Ahmed Boudaoui
- Laboratory of Mathematics Modeling and Applications, University of Adrar, Algeria
| | - Saif Ullah
- Department of Mathematics, University of Peshawar Khyber Pakhtunkhwa, Pakistan
| | - Fatma Bozkurt
- Department of Mathematics, Erciyes University, 38039 Kayseri, Turkey
| | - Thabet Abdeljawad
- Department of Mathematics and General Sciences, Prince Sultan University Riyadh, Saudi Arabia
- Department of Medical Research, China Medical University, Taichung 40402, Taiwan
- Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
| | - Manar A Alqudah
- Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
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Asamoah JKK, Owusu MA, Jin Z, Oduro FT, Abidemi A, Gyasi EO. Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana. CHAOS, SOLITONS, AND FRACTALS 2020; 140:110103. [PMID: 32834629 PMCID: PMC7351453 DOI: 10.1016/j.chaos.2020.110103] [Citation(s) in RCA: 91] [Impact Index Per Article: 22.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Revised: 07/06/2020] [Accepted: 07/09/2020] [Indexed: 05/17/2023]
Abstract
COVID-19 potentially threatens the lives and livelihood of people all over the world. The disease is presently a major health concern in Ghana and the rest of the world. Although, human to human transmission dynamics has been established, not much research is done on the dynamics of the virus in the environment and the role human play by releasing the virus into the environment. Therefore, investigating the human-environment-human by use of mathematical analysis and optimal control theory is relatively necessary. The dynamics of COVID-19 for this study is segregated into compartments as: Susceptible (S), Exposed (E), Asymptomatic (A), Symptomatic (I), Recovered (R) and the Virus in the environment/surfaces (V). The basic reproduction number R 0 without controls is computed. The application of Lyapunov's function is used to analyse the global stability of the proposed model. We fit the model to real data from Ghana in the time window 12th March 2020 to 7th May 2020, with the aid of python programming language using the least-squares method. The average basic reproduction number without controls,R 0 a , is approximately 2.68. An optimal control is formulated based on the sensitivity analysis. Numerical simulation of the model is also done to verify the analytic results. The admissible control set such as: effective testing and quarantine when boarders are opened, the usage of masks and face shields through media education, cleaning of surfaces with home-based detergents, practising proper cough etiquette and fumigating commercial areas; health centers is simulated in MATLAB. We used forward-backward sweep Runge-Kutta scheme which gave interesting results in the main text, for example, the cost-effectiveness analysis shows that, Strategy 4 (safety measures adopted by the asymptomatic and symptomatic individuals such as practicing proper coughing etiquette by maintaining a distance, covering coughs and sneezes with disposable tissues or clothing and washing of hands after coughing or sneezing) is the most cost-effective strategy among all the six control intervention strategies under consideration.
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Affiliation(s)
- Joshua Kiddy K Asamoah
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
- African Institute for Mathematical Sciences, Accra-Ghana
| | - Mark A Owusu
- African Institute for Mathematical Sciences, Accra-Ghana
| | - Zhen Jin
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, China
| | - F T Oduro
- African Institute for Mathematical Sciences, Accra-Ghana
- Kwame Nkrumah University of Science and Technology, Kumasi-Ghana
| | - Afeez Abidemi
- Department of Mathematical Sciences, Universiti Teknologi Malaysia, Johor, 81310 Johor Bahru, Malaysia
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Liu C, Kong L. Dynamics of an HIV model with cytotoxic T-lymphocyte memory. ADVANCES IN DIFFERENCE EQUATIONS 2020; 2020:581. [PMID: 33101401 PMCID: PMC7568027 DOI: 10.1186/s13662-020-03035-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 10/06/2020] [Indexed: 06/11/2023]
Abstract
We consider a four-dimensional HIV model that includes healthy cells, infected cells, primary cytotoxic T-lymphocyte response (CTLp), and secondary cytotoxic T-lymphocyte response (CTLe). The CTL memory generation depends on CD4+ T-cell help, and infection of CD4+ T cells results in impaired T-cell help. We show that the system has up to five equilibria. By the Routh-Hurwitz theorem and central manifold theorem we obtain some sufficient conditions for the local stability, globally stability of the equilibria, and the bifurcations. We still discover the bistability case where in the system there may coexist two stable equilibria or a stable equilibrium together with a stable limit cycle. Several numerical analyses are carried out to illustrate the validity of our theoretical results.
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Affiliation(s)
- Chunhua Liu
- School of Mathematics and Statistics, Yangtze Normal University, Fuling district, 408100 Chongqing city, P.R. China
| | - Lei Kong
- School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou, 550025 P.R. China
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