12 results
Search Results
2. Global stability of an SEIR epidemic model with vaccination.
- Author
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Wang, Lili and Xu, Rui
- Subjects
EPIDEMIOLOGICAL models ,VACCINATION ,MATRICES (Mathematics) ,MATHEMATICAL analysis ,COMPUTER simulation - Abstract
In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
3. Nonstandard Finite Difference Schemes for the Study of the Dynamics of the Babesiosis Disease.
- Author
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Dang, Quang A., Hoang, Manh T., Trejos, Deccy Y., and Valverde, Jose C.
- Subjects
FINITE differences ,BABESIOSIS ,MATHEMATICAL analysis ,LYAPUNOV functions ,COMPUTER simulation ,BASIC reproduction number - Abstract
In this paper, a discrete-time model for Babesiosis disease, given by means of nonstandard finite difference (NSFD) schemes, is first provided and analyzed. Mathematical analyses show that the provided NSFD schemes preserve the essential (qualitative) dynamical properties of the continuous-time model, namely, positivity and boundedness of the solutions, equilibria, and their stability properties. In particular, the global stability of the disease free equilibrium point is proved by using an appropriate Lyapunov function. As a relevant consequence, we get the dynamic consistency of NSFD schemes in relation to the continuous-time model. Numerical simulations are presented to support the validity of the established theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
4. Global Stability of a Three-Species Food-Chain Model with Diffusion and Nonlocal Delays.
- Author
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Zhang, Xiao, Xu, Rui, and Li, Zhe
- Subjects
FOOD chains ,STABILITY (Mechanics) ,REACTION-diffusion equations ,COMPUTER simulation ,MATHEMATICAL analysis ,SPATIO-temporal variation ,MATHEMATICAL variables - Abstract
In this paper, a three species reaction-diffusion food-chain system with nonlocal delays is investigated. Sufficient conditions are derived for the global stability of a positive steady state and boundary steady states of the system by using the energy function method. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
5. A mathematical analysis of Pine Wilt disease with variable population size and optimal control strategies.
- Author
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Khan, Muhammad Altaf, Khan, Rizwan, Khan, Yasir, and Islam, Saeed
- Subjects
- *
CONIFER wilt , *PLANT populations , *MATHEMATICAL analysis , *OPTIMAL control theory , *COMPUTER simulation , *PREVENTION - Abstract
The present paper describes the dynamics of the Pine Wilt disease with variable population size. The basic mathematical results for the model are presented. The stability analysis of both the disease-free and endemic cases are presented whenever R 0 lesser or greater than one, respectively. Further, an optimal control problem is formulated and the necessarily involved results are presented. Moreover, the numerical simulation of the optimal control problem with suggested control strategies for the possible eliminations of the infection in the pine trees population is presented. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
6. Dynamical behaviours of a delayed diffusive eco-epidemiological model with fear effect.
- Author
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Liu, Jia, Cai, Yongli, Tan, Jing, and Chen, Yeqin
- Subjects
- *
HOPF bifurcations , *MATHEMATICAL analysis , *SPATIAL systems , *NUMERICAL analysis , *COMPUTER simulation - Abstract
This paper concerned with a delayed diffusive eco-epidemiological model with fear effect. First, we discuss the existence and boundedness of the solution of the system. Then we give some conditions for the existence and stability of the nonnegative equilibria, and Turing instability. Furthermore, we choose the delay as bifurcation parameter to study Hopf bifurcation. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can induce the spatial pattern in the system. • We propose a delayed diffusive eco-epidemiological model with fear effect. • We have studied Hopf bifurcation and Turing bifurcation of the model. • We have discussed the global stability of the equilibria. • The results show that system can generate a wide variety of spatial patterns. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
7. Epidemic spreading and global stability of an SIS model with an infective vector on complex networks.
- Author
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Kang, Huiyan and Fu, Xinchu
- Subjects
- *
EPIDEMICS , *GLOBAL analysis (Mathematics) , *VECTOR analysis , *MATHEMATICAL analysis , *COMPUTER simulation , *MATHEMATICAL complexes , *MATHEMATICAL models - Abstract
In this paper, we present a new SIS model with delay on scale-free networks. The model is suitable to describe some epidemics which are not only transmitted by a vector but also spread between individuals by direct contacts. In view of the biological relevance and real spreading process, we introduce a delay to denote average incubation period of disease in a vector. By mathematical analysis, we obtain the epidemic threshold and prove the global stability of equilibria. The simulation shows the delay will effect the epidemic spreading. Finally, we investigate and compare two major immunization strategies, uniform immunization and targeted immunization. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
8. Global analysis of multiple routes of disease transmission on heterogeneous networks.
- Author
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Wang, Yi and Jin, Zhen
- Subjects
- *
INFECTIOUS disease transmission , *DISEASE prevalence , *MATHEMATICAL analysis , *IMMUNIZATION , *EQUILIBRIUM , *COMPUTER simulation - Abstract
Abstract: In this paper, we propose and study an SIS epidemic model with multiple transmission routes on heterogeneous networks. We focus on the dynamical evolution of the prevalence. Through mathematical analysis, we obtain the basic reproduction number by investigating the local stability of the disease-free equilibrium and also investigate the effects of various immunization schemes on disease spread. We further obtain that the disease will die out independent of the initial infections if the basic reproduction number is less than one, otherwise if the basic reproduction number is larger than one, the system converges to a unique endemic equilibrium, which is globally stable and thus the disease persists in the population. Our theoretical results are conformed by a series of numerical simulations and suggest a promising way for the control of infectious diseases with multiple routes. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
9. Mathematical analysis of a two-sex Human Papillomavirus (HPV) model.
- Author
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Omame, A., Umana, R. A., Okuonghae, D., and Inyama, S. C.
- Subjects
MATHEMATICAL analysis ,TRANSMISSION of papillomavirus diseases ,CONDOM use ,HUMAN sexuality ,COMPUTER simulation - Abstract
A two-sex deterministic model for Human Papillomavirus (HPV) that assesses the impact of treatment and vaccination on its transmission dynamics is designed and rigorously analyzed. The model is shown to exhibit the phenomenon of backward bifurcation, caused by the imperfect vaccine as well as the re-infection of individuals who recover from a previous infection, when the associated reproduction number is less than unity. Analysis of the reproduction number reveals that the impact of treatment on effective control of the disease is conditional, and depends on the sign of a certain threshold unlike when preventive measures are implemented (i.e. condom use and vaccination of both males and females). Numerical simulations of the model showed that, based on the parameter values used therein, a vaccine (with 75% efficacy) for male population with about 40% condom compliance by females will result in a significant reduction in the disease burden in the population. Also, the numerical simulations of the model reveal that with 70% condom compliance by the male population, administering female vaccine (with 45% efficacy) is sufficient for effective control of the disease. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
10. A mathematical analysis of Hopf-bifurcation in a prey-predator model with nonlinear functional response
- Author
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Assane Savadogo, Hamidou Ouedraogo, and Boureima Sangaré
- Subjects
Lyapunov function ,Functional response ,Global stability ,01 natural sciences ,symbols.namesake ,Numerical simulations ,QA1-939 ,Quantitative Biology::Populations and Evolution ,Uniqueness ,0101 mathematics ,Mathematics ,Hopf bifurcation ,Algebra and Number Theory ,Partial differential equation ,Prey-predator system ,Computer simulation ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,010101 applied mathematics ,Nonlinear system ,Hopf-bifurcation ,Ordinary differential equation ,symbols ,Analysis - Abstract
In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.
- Published
- 2021
11. Mathematical analysis of COVID-19 by using SIR model with convex incidence rate
- Author
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Ebrahem A. Algehyne and Rahim ud Din
- Subjects
Lyapunov function ,Computer simulation ,Differential equation ,Mathematical analysis ,Finite difference ,General Physics and Astronomy ,COVID-19 ,Nonstandard finite difference scheme ,Global stability ,SIR COVID model ,Stability (probability) ,Article ,Basic reproduction number ,lcsh:QC1-999 ,symbols.namesake ,Local stability ,Jacobian matrix and determinant ,symbols ,Epidemic model ,lcsh:Physics ,Mathematics - Abstract
This paper is about a new COVID-19 SIR model containing three classes; Susceptible S(t), Infected I(t), and Recovered R(t) with the Convex incidence rate. Firstly, we present the subject model in the form of differential equations. Secondly, “the disease-free and endemic equilibrium” is calculated for the model. Also, the basic reproduction number R 0 is derived for the model. Furthermore, the Global Stability is calculated using the Lyapunov Function construction, while the Local Stability is determined using the Jacobian matrix. The numerical simulation is calculated using the Non-Standard Finite Difference (NFDS) scheme. In the numerical simulation, we prove our model using the data from Pakistan. “Simulation” means how S(t), I(t), and R(t) protection, exposure, and death rates affect people with the elapse of time.
- Published
- 2021
12. Mathematical Analysis of a Fractional COVID-19 Model Applied to Wuhan, Spain and Portugal.
- Author
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Ndaïrou, Faïçal and Torres, Delfim F. M.
- Subjects
COVID-19 ,MATHEMATICAL analysis ,COMPUTER simulation - Abstract
We propose a qualitative analysis of a recent fractional-order COVID-19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations are performed to ensure stability and convergence of the disease free equilibrium point. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
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