scholarly journals A stochastic mathematical model of two different infectious epidemic under vertical transmission

2021 ◽  
Vol 19 (3) ◽  
pp. 2179-2192
Author(s):  
Xunyang Wang ◽  
◽  
Canyun Huang ◽  
Yixin Hao ◽  
Qihong Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Vertical Transmission ◽  
Biological Significance ◽  
Sufficient Conditions ◽  
Discussion Section ◽  
Stochastic Permanence ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Well Posed ◽  
Theoretical Results

<abstract><p>In this study, considering the effect of environment perturbation which is usually embodied by the alteration of contact infection rate, we formulate a stochastic epidemic mathematical model in which two different kinds of infectious diseases that spread simultaneously through both horizontal and vertical transmission are described. To indicate our model is well-posed and of biological significance, we prove the existence and uniqueness of positive solution at the beginning. By constructing suitable $ Lyapunov $ functions (which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation) and applying $ It\hat{o} $'s formula as well as $ Chebyshev $'s inequality, we also establish the sufficient conditions for stochastic ultimate boundedness. Furthermore, when some main parameters and all the stochastically perturbed intensities satisfy a certain relationship, we finally prove the stochastic permanence. Our results show that the perturbed intensities should be no greater than a certain positive number which is up-bounded by some parameters in the system, otherwise, the system will be surely extinct. The reliability of theoretical results are further illustrated by numerical simulations. Finally, in the discussion section, we put forward two important and interesting questions left for further investigation.</p></abstract>

Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

2020 ◽  
pp. 2050085
Author(s):  
Luyao Xin ◽  
Yingxin Guo ◽  
Quanxin Zhu
Keyword(s):  
Mathematical Model ◽  
White Noise ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Deterministic Case ◽  
Epidemic Dynamics ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Permanence In Mean ◽  
Theoretical Results

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual. Then, we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases. Moreover, in view of the association between susceptible and recovered individual perturbed by white noise, we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise. Finally, we have numerical simulations to demonstrate the correctness of obtained theoretical results.

scholarly journals Correlated Stochastic Epidemic Model for the Dynamics of SARS-CoV-2 with Vaccination

2021 ◽  
Author(s):  
Tahir Khan ◽  
Roman Ullah ◽  
Gul Zaman ◽  
Youssef Khatib
Keyword(s):  
Mathematical Model ◽  
Brownian Motion ◽  
Stochastic Model ◽  
Existence And Uniqueness ◽  
Human Population ◽  
Sufficient Conditions ◽  
Stochastic Epidemic ◽  
Stochastic Epidemic Model ◽  
Virus Spreading ◽  
Theoretical Results

Abstract We formulate a mathematical model has been proposed to describe the stochastic influence of SARS-CoV-2 virus with various sources of randomness and vaccination. We assume the various sources of ran-domness in each population groups by different Brownian motion. We develop the correlated stochastic model by taking into account the various sources of randomness by different Brownian motions and distributed the total human population in three groups of susceptible, infected and recovered with reservoir class. Because reservoir play a significant role in the transmission of SARS-CoV-2 virus spreading. Moreover, the vaccination of susceptible are also accorded. Once we formulate the correlated stochastic model, the existence and uniqueness of positive solution will be discussed to show the problem feasibility. The SARS-CoV-2 extinction as well as persistency will be also discussed and we will obtain the sufficient conditions for it. At the last all the theoretical results will be supported via numerical/graphical findings.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

scholarly journals Asymptotic Stability of Caputo Type Fractional Neutral Dynamical Systems with Multiple Discrete Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hai Zhang ◽  
Daiyong Wu ◽  
Jinde Cao
Keyword(s):  
Asymptotic Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Stability Criteria ◽  
Differential Systems ◽  
Discrete Delays ◽  
Transcendental Equations ◽  
The Stability ◽  
Theoretical Results

We discuss the delay-independent asymptotic stability of Caputo type fractional-order neutral differential systems with multiple discrete delays. Based on the algebraic approach and matrix theory, the sufficient conditions are derived to ensure the asymptotic stability for all time-delay parameters. By applying the stability criteria, one can avoid solving the roots of transcendental equations. The results obtained are computationally flexible and convenient. Moreover, an example is provided to illustrate the effectiveness and applicability of the proposed theoretical results.

Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

2019 ◽  
Vol 20 (2) ◽  
pp. 125-136
Author(s):  
A. M. Yousef ◽  
S. Z. Rida ◽  
Y. Gh. Gouda ◽  
A. S. Zaki
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Theoretical Results

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

scholarly journals Adaptive Guaranteed-Performance Consensus Control for Multi-Agent Systems with an Adjustable Convergence Speed

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Haiying Ma ◽  
Xiao Jia ◽  
Ning Cai ◽  
Jianxiang Xi
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Convergence Speed ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Consensus Control ◽  
Control Gain ◽  
Multi Agent ◽  
The Stability ◽  
Theoretical Results

In this paper, adaptive guaranteed-performance consensus control problems for multiagent systems with an adjustable convergence speed are investigated. A novel adaptive guaranteed-performance consensus protocol is proposed, where the communication weights can be adaptively regulated. By the state space decomposition method and the stability theory, sufficient conditions for guaranteed-performance consensus are obtained and the guaranteed-performance cost is determined. Moreover, the lower bound of the convergence coefficient for multiagent systems is deduced, which is linearly adjustable approximately by changing the adaptive control gain. Finally, simulation examples are introduced to demonstrate theoretical results.

scholarly journals A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia

2020 ◽  
Author(s):  
Lorand Gabriel Parajdi ◽  
Radu Precup ◽  
Eduard Alexandru Bonci ◽  
Ciprian Tomuleasa
Keyword(s):  
Mathematical Model ◽  
Stem Cells ◽  
Bone Marrow ◽  
Stability Analysis ◽  
Myeloid Leukemia ◽  
Transition Process ◽  
Two Dimensional ◽  
The Stability ◽  
Theoretical Results

A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

scholarly journals Preventing extinction in Rastrelliger brachysoma using an impulsive mathematical model

2021 ◽  
Vol 7 (1) ◽  
pp. 1-24
Author(s):  
Din Prathumwan ◽  
◽  
Kamonchat Trachoo ◽  
Wasan Maiaugree ◽  
Inthira Chaiya ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Population Density ◽  
Upper Bound ◽  
Existence And Uniqueness ◽  
Periodic Behavior ◽  
Toxic Environment ◽  
Pacific Mackerel ◽  
The Stability ◽  
Theoretical Results

<abstract><p>In this paper, we proposed a mathematical model of the population density of Indo-Pacific mackerel (<italic>Rastrelliger brachysoma</italic>) and the population density of small fishes based on the impulsive fishery. The model also considers the effects of the toxic environment that is the major problem in the water. The developed impulsive mathematical model was analyzed theoretically in terms of existence and uniqueness, positivity, and upper bound of the solution. The obtained solution has a periodic behavior that is suitable for the fishery. Moreover, the stability, permanence, and positive of the periodic solution are investigated. Then, we obtain the parameter conditions of the model for which Indo-Pacific mackerel conservation might be expected. Numerical results were also investigated to confirm our theoretical results. The results represent the periodic behavior of the population density of the Indo-Pacific mackerel and small fishes. The outcomes showed that the duration and quantity of fisheries were the keys to prevent the extinction of Indo-Pacific mackerel.</p></abstract>

Hopf Bifurcation of a Generalized Delay-Induced Predator–Prey System with Habitat Complexity

2020 ◽  
Vol 30 (06) ◽  
pp. 2050082
Author(s):  
Zhihui Ma
Keyword(s):  
Hopf Bifurcation ◽  
Habitat Complexity ◽  
Sufficient Conditions ◽  
Explicit Formulas ◽  
Predator Prey ◽  
Dynamical Behaviors ◽  
Prey System ◽  
The Stability ◽  
Theoretical Results ◽  
Positivity And Boundedness

A delay-induced nonautonomous predator–prey system with variable habitat complexity is proposed based on mathematical and ecological issues, and this system is more realistic than the published models. Firstly, the permanence of the nonautonomous predation system is studied and some sufficient conditions are obtained. Secondly, the dynamical behaviors of the corresponding autonomous predation system are investigated, including the positivity and boundedness, and local and global stabilities. Thirdly, the properties of Hopf bifurcation of the autonomous predation system without/with delay are investigated and the explicit formulas which determine the stability and the direction of periodic solutions are obtained. Finally, a numerical example is given to test our theoretical results.

Analysis of within-host CHIKV dynamics models with general incidence rate

2018 ◽  
Vol 11 (05) ◽  
pp. 1850062 ◽  
Author(s):  
Ahmed M. Elaiw ◽  
Taofeek O. Alade ◽  
Saud M. Alsulami
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Nonlinear Function ◽  
Steady States ◽  
Positive Steady States ◽  
Latently Infected ◽  
The Stability ◽  
Dynamics Models ◽  
Theoretical Results

In this paper we study the stability analysis of two within-host Chikungunya virus (CHIKV) dynamics models. The incidence rate between the CHIKV and the uninfected monocytes is modeled by a general nonlinear function. The second model considers two types of infected monocytes (i) latently infected monocytes which do not generate CHIKV and (ii) actively infected monocytes which produce the CHIKV particles. Sufficient conditions are found which guarantee the global stability of the positive steady states. Using the Lyapunov function, we established the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations.

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