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 Global Dynamics and Sensitivity Analysis of a Vector-Host-Reservoir Model

2016 ◽  
Vol 21 (2) ◽  
pp. 120
Author(s):  
Ibrahim M. ELmojtaba ◽  
Santanu Biswas ◽  
Joydev Chattopadhyay
Keyword(s):  
Sensitivity Analysis ◽  
Positive Equilibrium ◽  
Model Parameters ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Animal Reservoir ◽  
Globally Asymptotically Stable ◽  
Numerical Result ◽  
Perform Sensitivity Analysis ◽  
Host Reservoir

The role of animal reservoir in the disease dynamics is not yet properly studied. In the present investigation a mathematical model of a vector-host-reservoir is proposed and analyzed to observe the global dynamics of the disease. We observe that the disease free equilibrium is globally asymptotically stable if the basic reproduction number ( ) is less than unity whereas unique positive equilibrium is globally asymptotically stable if and transcritical bifurcation occurs at . Our numerical result suggests that the biting rate plays an important role for the propagation of the disease and the recovery rate has not such important contribution towards eradication of the disease. We also perform sensitivity analysis of the model parameters and the results suggest that the death rate of reservoir may be used as a control parameter to eradicate the disease. 

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 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.

scholarly journals Dynamics of A Multi-stage Epidemic Model with and without Treatment

2020 ◽  
Vol 8 (5) ◽  
pp. 5293-5300
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Dynamical Behaviour ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, a non-linear mathematical model is proposed with the thought of treatment to depict the spread of infectious illness and assessed with three contamination stages. We talk about the dynamical behaviour and analytical study of the framework for the mathematical model which shows that it has two non-negative equilibrium points i.e., disease-free equilibrium (DFE) and interior(endemic) equilibrium. The outcomes show that the dynamical behaviour of the model is totally determined by the basic reproduction number. For the basic reproduction number , the disease-free equilibrium is locally as well as globally asymptotically stable under a particular parameter set. In case , the model at the interior equilibrium is locally as well as globally asymptotically stable. Finally, numerical solutions of the model corroborate the analytical results and facilitate a sensitivity analysis of the model parameters.

scholarly journals A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response

2014 ◽  
Vol 9 ◽  
pp. 53-68 ◽  
Author(s):  
B. El Boukari ◽  
N. Yousfi
Keyword(s):  
Reproduction Number ◽  
Equation Model ◽  
Asymptotically Stable ◽  
Differential Equation Model ◽  
Globally Asymptotically Stable ◽  
Intracellular Delay ◽  
Immunodeficiency Virus ◽  
Delay Differential ◽  
Theoretical Results ◽  
Disease Free

In this work we investigate a new mathematical model that describes the interactions betweenCD4+ T cells, human immunodeficiency virus (HIV), immune response and therapy with two drugs.Also an intracellular delay is incorporated into the model to express the lag between the time thevirus contacts a target cell and the time the cell becomes actively infected. The model dynamicsis completely defined by the basic reproduction number R0. If R0 ≤ 1 the disease-free equilibriumis globally asymptotically stable, and if R0 > 1, two endemic steady states exist, and their localstability depends on value of R0. We show that the intracellular delay affects on value of R0 becausea larger intracellular delay can reduce the value of R0 to below one. Finally, numerical simulationsare presented to illustrate our theoretical results.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

scholarly journals Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Hailay Weldegiorgis Berhe ◽  
Oluwole Daniel Makinde ◽  
David Mwangi Theuri
Keyword(s):  
Sensitivity Analysis ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Nonlinear Least Squares ◽  
Model Parameters ◽  
Nonlinear Least Squares Problem ◽  
The Stability ◽  
Diarrhea Disease ◽  
Effective Transmission ◽  
Disease Free

In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease-free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for R0>1. The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is R0=1.1208. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (βh). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.

Stability analysis and optimal control of an epidemic model with vaccination

2015 ◽  
Vol 08 (03) ◽  
pp. 1550030 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Epidemic Model ◽  
Asymptotically Stable ◽  
Control Pair ◽  
Globally Asymptotically Stable ◽  
The Stability ◽  
The Cost ◽  
Objective Functional ◽  
Disease Free

In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number (R0) of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0when R0< 1. When R0> 1 endemic equilibrium E1exists and the system becomes locally asymptotically stable at E1under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.

scholarly journals Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 328 ◽  
Author(s):  
Yanli Ma ◽  
Jia-Bao Liu ◽  
Haixia Li
Keyword(s):  
Lyapunov Function ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

Mathematical Study of a Class of Epidemiological Models with Multiple Infectious Stages

2020 ◽  
Vol 21 (3-4) ◽  
pp. 259-274
Author(s):  
S. Bowong ◽  
A. Temgoua ◽  
Y. Malong ◽  
J. Mbang
Keyword(s):  
Theoretical Study ◽  
Reproduction Number ◽  
Communicable Disease ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Epidemiological Models ◽  
Mathematical Study ◽  
Globally Asymptotically Stable ◽  
Disease Free

AbstractThis paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number $\mathcal R_0$ that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever $\mathcal R_0 \leq 1$, while when $\mathcal R_0 \gt 1$, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. A case study for tuberculosis (TB) is considered to numerically support the analytical results.

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