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.

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 sensitivity analysis, probabilistic calibration, and predictive assessment for the Data Assimilation Linked Ecosystem Carbon model

2014 ◽  
Vol 7 (5) ◽  
pp. 6893-6948
Author(s):  
C. Safta ◽  
D. Ricciuto ◽  
K. Sargsyan ◽  
B. Debusschere ◽  
H. N. Najm ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Data Assimilation ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Forest Site ◽  
Carbon Cycle Model ◽  
Global Sensitivity ◽  
Predictive Skill ◽  
Ecosystem Carbon

Abstract. In this paper we propose a probabilistic framework for an uncertainty quantification study of a carbon cycle model. A Global Sensitivity Analysis (GSA) study indicates the parameters and parameter couplings that are important at different times of the year for Quantities of Interest obtained with the Data Assimilation Linked Ecosystem Carbon (DALEC) model. We then employ a Bayesian approach to calibrate the parameters of DALEC using net ecosystem exchange observations at the Harvard Forest site. The calibration exercise is guided by GSA and by Fisher information matrix results that quantify the amount of information carried by the experimental data about specific model parameters. The calibration results are employed in the second part of the paper to assess the predictive skill of the model via posterior predictive checks. These checks show a better performance for the non-steady state model during the growing season compared to the one employing steady state assumptions. Overall, this study leads to a 40% improvement in the predictive skill of DALEC and highlights the importance of considering correlations in the model parameters as informed by the data.

Estimation of Cumene Cracking Reaction-Diffusion Model Parameters: Uniqueness and Parametric Sensitivity Analysis

2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Peter Schwan ◽  
Klaus P Möller
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Parameter Estimates ◽  
Physical Parameters ◽  
Model Parameters ◽  
Response Curves ◽  
Cumene Cracking ◽  
Irreversible Reaction ◽  
Reaction Diffusion Model ◽  
Order Of Magnitude

The pulse response of cumene cracking over ZSM5 extrudates has been measured using a Jetloop recycle reactor. A model assuming first order irreversible reaction with constant macro-pore diffusivity and linear adsorption was used to describe the response curves of the reactants and products. The model parameters adsorption, diffusion and reaction rate are in general highly correlated. Relationships for regions of parameter insensitivity and correlation functions between dependent parameters are given. With the aid of independent measurement of adsorption, a sensitivity analysis and a similarity analysis between equations, it was possible to reduce the 7 parameter model into a 2 parameter model for conditions of strong diffusion limitation observed in these experiments. Although good model fits could be achieved, a high degree of uncertainty in the parameter estimates remained, which reflects the high correlation of the physical parameters. Comparison with steady state results shows that the transient diffusivity for cumene is approximately equal to the Knudsen diffusivity, but an order of magnitude lower than the steady state diffusivity. The transient Thiele modulus for cumene was an order of magnitude higher than the steady state value.

scholarly journals Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Wei Zhang ◽  
Juan Zhang ◽  
Yong-Ping Wu ◽  
Li Li
Keyword(s):  
Steady State ◽  
Global Stability ◽  
Dairy Cows ◽  
Immune Cells ◽  
Steady States ◽  
The Body ◽  
Infection Dose ◽  
The One ◽  
Immunological Threshold ◽  
Disease Free

As we all know, bacteria is different from virus which with certain types can be killed by the immune cells in the body. The brucellosis, a bacterial disease, can invade the body by indirect transmission from environment, which has not been researched by combining with immune cells. Considering the effects of immune cells, we put a minimum infection dose of brucellosis invading into the dairy cows as an immunological threshold and get a switch model. In this paper, we accomplish a thorough dynamics analysis of a SEIB switch model. On the one hand, we can get a disease-free and bacteria-free steady state and up to three endemic steady states which may be thoroughly analyzed in different cases of a minimum infection dose in a switch model. On the other hand, we calculate the basic reproduction number R0 and know that the disease-free and bacteria-free steady state is a global stability when R0<1, and the one of the endemic steady state is a conditionally global stability when R0>1. We find that different amounts of R0 may lead to different steady states of brucellosis, and considering the effects of immunology is more serious in mathematics and 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.

DYNAMICS OF AN INFECTIOUS DISEASE IN THE PRESENCE OF SATURATED MEDICAL TREATMENT OF HOLLING TYPE III AND SELF-PROTECTION

2021 ◽  
pp. 1-45
Author(s):  
ROSHAN MANDALE ◽  
ANUJ KUMAR ◽  
D. K. K. VAMSI ◽  
PRASHANT K. SRIVASTAVA
Keyword(s):  
Sensitivity Analysis ◽  
Cost Effective ◽  
Model Parameters ◽  
Optimal Controls ◽  
Existence And Stability ◽  
Huge Impact ◽  
Effective Choice ◽  
Two Parameters ◽  
Self Protection ◽  
Saturated Treatment

A nonlinear SEIR model is formulated and analyzed. This model accounts for three important interventions — the saturated treatment on infective individuals, the screening on the exposed individuals and the information induced self-protection on susceptible individuals. Existence and stability of equilibria are discussed. A sensitivity analysis for the model parameters is performed and we identified the parameters which are more sensitive to the model system. The sensitivity analysis is further followed up with the two parameters heat plot that determines the regions for the parametric values in which the system is either stable or unstable. Further, an optimal control problem is formulated by considering screening and treatment as control variables and corresponding cost functional is constructed. Using Pontryagin’s Maximum Principle, paths of optimal controls are obtained analytically. A comparative study is conducted numerically to explore and analyze analytical results. We note that in absence of treatment, screening policy may be a cost-effective choice to keep a tab on the disease. However, comprehensive effect of both screening and treatment has a huge impact, which is highly effective and least expensive. It is also noted that treatment is effective for mild epidemic whereas screening has a significant effect on the disease burden while epidemic is severe. For a range of basic reproduction number, effect of self-protection and saturation in treatment is also explored numerically.

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.

Holdup and holdup profiles in the reciprocating plate extractor VPE

1990 ◽  
Vol 55 (11) ◽  
pp. 2648-2661 ◽  
Author(s):  
Helena Sovová ◽  
Vladislav Bízek ◽  
Jaroslav Procházka
Keyword(s):  
Steady State ◽  
Experimental Results ◽  
Model Parameters ◽  
Dispersed Phase ◽  
Pulse Form ◽  
Sieve Plates

In this work measurements of mean holdup of dispersed phase, of axial holdup profiles and of flooding points in a reciprocating plate contactor with both the VPE-type plates and the sieve plates were carried out. The experimental results were compared with a monodisperse model of steady-state column hydrodynamics and the model parameters were evaluated. Important differences in the behaviour of the two plate types could be identified. Comparison was also made between two reciprocating drives of different pulse form.

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