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 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 Dynamics of a Market Share Model for Enterprises with Coopetition Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Mingxia Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Market Share ◽  
Deterministic Model ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Share Model ◽  
Global Threshold ◽  
Globally Attractive ◽  
Globally Stable

A deterministic model is used to study the change of the market share with coopetition strategy for enterprises. The model takes into consideration both coopetition enterprises and other enterprises, and the coopetition thresholdR0is identified and global dynamics are completely determined byR0. It shows thatR0is a global threshold parameter in the sense that ifR0<1, the coopetition free equilibrium is globally stable and the market share of coopetition enterprises tends to zero, whereas ifR0>1, there is a unique coopetition equilibrium which is globally attractive with some conditions, and thus the market share of coopetition enterprises tends to a steady state value. By some sensitivity analysis ofR0on parameters, we conclude that the size of the coopetition thresholdR0and coopetition equilibrium depended on the cooperation competitiveness of coopetition enterprises.

scholarly journals Effect of Undecided and Swing Voters on The Dynamics Voters Model in Presidential Elections

2021 ◽  
Vol 2123 (1) ◽  
pp. 012012
Author(s):  
B. Yong
Keyword(s):  
Sensitivity Analysis ◽  
Presidential Elections ◽  
Equilibrium Points ◽  
Model Parameters ◽  
Threshold Parameter ◽  
Sensitive Parameter ◽  
Swing Voters

Abstract In this paper, we construct the NUS1S2A voters model of two political fanaticism figures which involves undecided and swing voters. We determine the equilibrium points and the threshold parameter of the voters model. We also perform a sensitivity analysis for the threshold number to determine the importance of model parameters. The results of the sensitivity analysis show that the rate of transfer from neutral voters to undecided and swing voters is not the most negative sensitive parameter of the model, even though an increase in its parameter will cause a decrease in voter interest in voting in the presidential elections.

scholarly journals MODELING KENYA’S DOMESTIC RADICALIZATION LIKE A DISEASE BY INCORPORATING EFFORTS OF CLERGIES, REHABILITATION CENTERS AND JUSTICE SYSTEM

2017 ◽  
Keyword(s):  
Sensitivity Analysis ◽  
Legal System ◽  
Justice System ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Intervention Strategy ◽  
Numerical Results ◽  
Rehabilitation Centers ◽  
Analytical Results

This study presents a deterministic model for domestic radicalization process in Kenya and uses the model to assess the effect of efforts of good clergies, rehabilitation centers and legal system in lowering radicalization burden. The likelihood of other drivers of radicalization to individuals who are not religious fanatics was considered. The possibility of individuals in rehabilitated subclass quitting back to violent class was considered. The equilibrium points were computed, their stabilities investigated and important thresholds determining the progression of the radicalization computed. The sensitivity analysis of control reproduction number indicates that high intervention rates hold is likely to reduce the radicalization burden. The results indicate that use of good clergies to assist individuals’ radicalized but peaceful, to recover is the best intervention strategy. Estimated numerical results and simulations were carried to confirm analytical results.

scholarly journals A Stochastic Harmonic Oscillator Temperature Model for the Valuation of Weather Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2890
Author(s):  
Alessio Giorgini ◽  
Rogemar S. Mamon ◽  
Marianito R. Rodrigo
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Estimation ◽  
Harmonic Oscillator ◽  
Numerical Simulations ◽  
Model Parameters ◽  
Call Option ◽  
Temperature Model ◽  
Option Prices ◽  
Harmonic Oscillator Model ◽  
Temperature Dynamics

Stochastic processes are employed in this paper to capture the evolution of daily mean temperatures, with the goal of pricing temperature-based weather options. A stochastic harmonic oscillator model is proposed for the temperature dynamics and results of numerical simulations and parameter estimation are presented. The temperature model is used to price a one-month call option and a sensitivity analysis is undertaken to examine how call option prices are affected when the model parameters are varied.

Dynamics of an ecological system

2019 ◽  
Vol 10 (4) ◽  
pp. 355-376
Author(s):  
Shashi Kant
Keyword(s):  
Saddle Point ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Local Stability ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Prey Refuge ◽  
Trivial Equilibrium ◽  
Stability Results ◽  
Predator System

AbstractIn this paper, we investigate the deterministic and stochastic prey-predator system with refuge. The basic local stability results for the deterministic model have been performed. It is found that all the equilibrium points except the positive coexisting equilibrium point of the deterministic model are independent of the prey refuge. The trivial equilibrium point, predator free equilibrium point and prey free equilibrium point are always unstable (saddle point). The existence and local stability of the coexisting equilibrium point is related to the prey refuge. The permanence and extinction conditions of the proposed biological model have been studied rigourously. It is observed that the stochastic effect may be seen in the form of decaying of the species. The numerical simulations for different values of the refuge values have also been included for understanding the behavior of the model graphically.

scholarly journals Stability of a Nonlinear Stochastic Epidemic Model with Transfer from Infectious to Susceptible

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yanmei Wang ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Method ◽  
Deterministic Model ◽  
Vital Role ◽  
Nonlinear Incidence Rate ◽  
Sirs Model ◽  
Stochastic Epidemic ◽  
Almost Surely Exponential Stability ◽  
Theoretical Results ◽  
Disease Free

We investigate a stochastic SIRS model with transfer from infectious to susceptible and nonlinear incidence rate. First, using stochastic stability theory, we discuss stochastic asymptotic stability of disease-free equilibrium of this model. Moreover, if the transfer rate from infectious to susceptible is sufficiently large, disease goes extinct. Then, we obtain almost surely exponential stability of disease-free equilibrium, which implies that noises can lead to extinction of disease. By the Lyapunov method, we give conditions to ensure that the solution of this model fluctuates around endemic equilibrium of the corresponding deterministic model in average time. Furthermore, numerical simulations show that the fluctuation increases with increase in noise intensity. Finally, these theoretical results are verified by numerical simulations. Hence, noises play a vital role in epidemic transmission. Our results improve and extend previous related results.

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.

scholarly journals Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Fulgensia Kamugisha Mbabazi ◽  
J. Y. T. Mugisha ◽  
Mark Kimathi
Keyword(s):  
Sensitivity Analysis ◽  
Antibiotic Resistance ◽  
Steady State ◽  
Global Stability ◽  
Influenza A ◽  
Pneumococcal Pneumonia ◽  
Effective Rate ◽  
Model Parameters ◽  
Saturated Treatment ◽  
Disease Free

Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, R0, is computed using the next generation matrix method. The results show that if R0<1, the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if R0>1 the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of R0 on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of R0 on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.

THE DYNAMICS OF A DISCRETE SEIT MODEL WITH AGE AND INFECTION AGE STRUCTURES

2012 ◽  
Vol 05 (03) ◽  
pp. 1260004 ◽  
Author(s):  
HUI CAO ◽  
YANNI XIAO ◽  
YICANG ZHOU
Keyword(s):  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Disease Spread ◽  
Threshold Parameter ◽  
Infection Age ◽  
The Stability ◽  
Globally Stable ◽  
Disease Free ◽  
The Basic Reproduction Number ◽  
Age Structures

Age and infection age have significant influence on the transmission of infectious diseases, such as HIV/AIDS and TB. A discrete SEIT model with age and infection age structures is formulated to investigate the dynamics of the disease spread. The basic reproduction number R0 is defined and used as the threshold parameter to characterize the disease extinction or persistence. It is shown that the disease-free equilibrium is globally stable if R0 < 1, and it is unstable if R0 > 1. When R0 > 1, there exists an endemic equilibrium, and the disease is uniformly persistent. The stability of the endemic equilibrium is investigated numerically.

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