scholarly journals Modeling the Parasitic Filariasis Spread by Mosquito in Periodic Environment

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yan Cheng ◽  
Xiaoyun Wang ◽  
Qiuhui Pan ◽  
Mingfeng He
Keyword(s):  
Sensitivity Analysis ◽  
Periodic Solution ◽  
Numerical Simulations ◽  
Parasitic Infection ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Periodic Environment ◽  
Disease Free

In this paper a mosquito-borne parasitic infection model in periodic environment is considered. Threshold parameterR0is given by linear next infection operator, which determined the dynamic behaviors of system. We obtain that whenR0<1, the disease-free periodic solution is globally asymptotically stable and whenR0>1by Poincaré map we obtain that disease is uniformly persistent. Numerical simulations support the results and sensitivity analysis shows effects of parameters onR0, which provided references to seek optimal measures to control the transmission of lymphatic filariasis.

scholarly journals Analysis of an HIV - HCV simultaneous infection model with time delay

2021 ◽  
pp. 1-11
Author(s):  
Adamu Shitu Hassan ◽  
Nafiu Hussaini
Keyword(s):  
Hepatitis C Virus ◽  
Hepatitis C ◽  
Time Delay ◽  
Numerical Simulations ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Delay Model ◽  
Globally Asymptotically Stable ◽  
Simultaneous Infection ◽  
Disease Free

A novel mathematical delay model for simultaneous infection of HIV and hepatitis C virus is formulated and dynamically analyzed. Basic properties of the model are established and proved. Basic reproductive threshold is systematically calculated as the maximum of three subthreshold parameters. A disease free equilibrium is determined to be globally asymptotically stable for all values of the delay when the threshold is less than unity. However, when the threshold is greater than one, endemic equilibrium emerged which is shown to be locally asymptotically stable for any length of delay. Although the delay has no effect on stabilities of equilibria points, however, it is found to reduce the infectivity of the viruses as the length of the delay is increased. Epidemiological interpretations of the results and numerical simulations illustrating them are given.

AN SIQS INFECTION MODEL WITH NONLINEAR AND ISOLATION

2008 ◽  
Vol 01 (02) ◽  
pp. 239-245
Author(s):  
YANG XIUXIANG ◽  
XUE CHUNRONG
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Liapunov Function ◽  
Threshold Value ◽  
Infection Model ◽  
Stable Theory ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Local Disease ◽  
Disease Free

By means of asymptotically stable theory and infection model theory of ordinary differential equation, we do research on SIQS model with nonlinear and isolation. Firstly, we obtain the existence of threshold value R0 of disease-free equilibration point and local disease equilibration point. Secondly, we prove disease-free equilibration point is locally asymptotically stable when R0 < 1, and local disease equilibration point is locally asymptotically stable when R0 > 1. Furthermore, we have disease-free equilibration point and local disease equilibration point are globally asymptotically stable with the help of Liapunov function. Lastly, we explain at the point of biology.

scholarly journals Stability and Sensitivity Analysis of Yellow Fever Dynamics

2019 ◽  
Vol 4 (12) ◽  
pp. 159-166
Author(s):  
Henry Otoo ◽  
S. Takyi Appiah ◽  
D. Arhinful
Keyword(s):  
Sensitivity Analysis ◽  
Yellow Fever ◽  
Northern Region ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Human Beings ◽  
African Countries ◽  
Globally Asymptotically Stable ◽  
Linear Ordinary Differential Equations ◽  
Disease Free

 Several West African countries have recently reported of Yellow Fever outbreaks. Ghana recently recorded an outbreak which lead to the death of three (3) people in the West Gonja District of the Northern Region. These indicate the re-emergence of the deadly disease. This research proposes a deterministic mathematical model through non-linear ordinary differential equations in order to gain an accurate insight into the dynamics of yellow fever between human beings and the vector Aedes mosquito in an unvaccinated area for the purpose of controlling the disease. The disease threshold parameter was obtained using the next generation matrix. The Gerschgorin theorem proved the disease-Free equilibrium and the Endemic equilibrium to be locally asymptotically stable for  and  respectively. The Lyapunov function proved the disease-Free Equilibrium to be globally asymptotically stable for . In order to study the effect of the model parameters to , the sensitivity analysis of the basic reproduction number with respect to epidemiological parameters was performed.

scholarly journals Modeling the Effect of External Computers and Removable Devices on a Computer Network with Heterogeneous Immunity

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Walaa S. Bahashwan ◽  
Salma M. Al-Tuwairqi
Keyword(s):  
Sensitivity Analysis ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Computer Network ◽  
Asymptotically Stable ◽  
Virus Spread ◽  
Globally Asymptotically Stable ◽  
Virus Prevalence ◽  
The Impact ◽  
Insight Into

This paper intends to investigate the impact of external computers and removable devices on virus spread in a network with heterogeneous immunity. For that purpose, a new dynamical model is presented and discussed. Theoretical analysis reveals the existence of a unique viral equilibrium that is locally and globally asymptotically stable with no criteria. This result implies that efforts to eliminate viruses are not possible. Therefore, sensitivity analysis is performed to have more insight into parameters’ impact on virus prevalence. As a result, strategies are suggested to contain virus spread to an acceptable level. Finally, to rationalize the analytical results, we execute some numerical simulations.

scholarly journals Deterministic and Stochastic Models of the Transmission Dynamics of Chicken Pox.

2019 ◽  
Vol 1 ◽  
pp. 184-192
Author(s):  
Bright O Osu ◽  
O Andrew ◽  
A I Victory
Keyword(s):  
Stochastic Model ◽  
Numerical Simulations ◽  
Stochastic Models ◽  
Deterministic Model ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Chicken Pox ◽  
Number Of Individuals ◽  
Disease Free

In this work a deterministic and stochastic model is developed and used to investigate the transmission dynamics of chicken pox. The models involve the Susceptible, Vaccinated, Exposed, Infectious and Recovered individuals. In the deterministic model the Disease free Equilibrium is computed and proved to be globally asymptotically stable when R0 < 1. The deterministic model is transformed into a stochastic model which was solved using the Euler Maruyama method. Numerical simulations of the stochastic Model show that as the vaccine rate wanes, the number of individuals susceptible to the chicken pox epidemic increases.

scholarly journals Mathematical Analysis of Rabies Infection

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
C. S. Bornaa ◽  
Baba Seidu ◽  
M. I. Daabo
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Mathematical Analysis ◽  
Asymptotically Stable ◽  
Local Sensitivity ◽  
Globally Asymptotically Stable ◽  
Local Sensitivity Analysis ◽  
Disease Free

A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever ℛ0≤1. Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy.

A mathematical model of cholera in a periodic environment with control actions

2020 ◽  
Vol 13 (04) ◽  
pp. 2050025
Author(s):  
G. Kolaye ◽  
I. Damakoa ◽  
S. Bowong ◽  
R. Houe ◽  
D. Békollè
Keyword(s):  
Control Strategies ◽  
Impulsive Differential Equations ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Periodic Environment ◽  
Control Actions ◽  
Number Formula ◽  
Classical Control ◽  
The Impact ◽  
Disease Free

In this paper, we studied the impact of sensitization and sanitation as possible control actions to curtail the spread of cholera epidemic within a human community. Firstly, we combined a model of Vibrio Cholerae with a generic SIRS cholera model. Classical control strategies in terms of the sensitization of population and sanitation are integrated through the impulsive differential equations. Then we presented the theoretical analysis of the model. More precisely, we computed the disease free equilibrium. We derive the basic reproduction number [Formula: see text] which determines the extinction and the persistence of the infection. We show that the trivial disease-free equilibrium is globally asymptotically stable whenever [Formula: see text], while when [Formula: see text], the trivial disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. Theoretical results are supported by numerical simulations, which further suggest that the control of cholera should consider both sensitization and sanitation, with a strong focus on the latter.

scholarly journals Dynamics of Toxoplasmosis Disease in Cats population with vaccination

2021 ◽  
pp. 17-25
Author(s):  
Idris Babaji Muhammad ◽  
Salisu Usaini
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Simulations ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Vaccination Rate ◽  
Steady States ◽  
Model Parameters ◽  
Threshold Parameter ◽  
Globally Stable ◽  
Disease Free

We extend the deterministic model for the dynamics of toxoplasmosis proposed by Arenas et al. in 2010, by separating vaccinated and recovered classes. The model exhibits two equilibrium points, the disease-free and endemic steady states. These points are both locally and globally stable asymptotically when the threshold parameter Rv is less than and greater than unity, respectively. The sensitivity analysis of the model parameters reveals that the vaccination parameter $\pi$ is more sensitive to changes than any other parameter. Indeed, as expected the numerical simulations reveal that the higher the vaccination rate of susceptible individuals the smaller the value of the threshold Rv (i.e., increase in $\pi$ results in the decrease in Rv , leading to the eradication of toxoplasmosis in cats population.

scholarly journals Co-infection Model Formulation to Evaluate the Transmission Dynamics of Malaria and Dengue Fever Virus

2020 ◽  
Vol 24 (7) ◽  
pp. 1187-1195
Author(s):  
T.J. Oluwafemi ◽  
N.I. Akinwande ◽  
R.O. Olayiwola ◽  
A.F. Kuta ◽  
E. Azuaba
Keyword(s):  
Dengue Fever ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Infection Dynamics ◽  
Reduction Number ◽  
Result Show ◽  
Disease Free

A mathematical model of the co-infection dynamics of malaria and dengue fever condition is formulated. In this work, the Basic reduction number is computed using the next generation method. The diseasefree equilibrium (DFE) point of the model is obtained. The local and global stability of the disease-free equilibrium point of the model is established. The result show that the DFE is locally asymptotically stable if the basic reproduction number is less than one but may not be globally asymptotically stable. Keywords: Malaria; Dengue Fever; Co-infection; Basic reproduction number; Disease-Free equilibrium

scholarly journals Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

2021 ◽  
Vol 83 (4) ◽  
Author(s):  
Mahmoud A. Ibrahim ◽  
Attila Dénes
Keyword(s):  
Zika Virus ◽  
Reproduction Number ◽  
Virus Disease ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

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