scholarly journals Modeling Tuberculosis Among Healthcare Workers

2019 ◽  
Vol 5 (2) ◽  
pp. 186-196
Author(s):  
T.S. Faniran ◽  
A.O. Falade ◽  
T.O. Alakija
Keyword(s):  
Sensitivity Analysis ◽  
Equilibrium Point ◽  
Healthcare Workers ◽  
Compliance Rate ◽  
Transmission Dynamics ◽  
Infectious Period ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Susceptible Population ◽  
The Impact

AbstractA mathematical model for transmission dynamics of tuberculosis among healthcare workers is formulated. Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis bacteria that affect the lungs of a host. Previous research had concentrated on mathematical modeling of transmission dynamics of tuberculosis without considering the impact of compliance rate to particulate respirator by healthcare workers on the transmission. Therefore, how compliance rate to particulate respirator reduces the transmission of tuberculosis is an active question, and we develop a new system of ordinary differential equations that explicitly explores the impact of compliance rate to particulate respirator by healthcare workers upon transmission. Rigorous analysis of the model shows that the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number, Ro < 1. This is established through the analysis of characteristic equation. Basic reproduction, Ro is the number of new cases that an existing case generates on average over the infectious period in a susceptible population. We also show that the endemic equilibrium point is locally asymptotically stable for Ro > 1, by using Routh-Hurwitz criteria for stability. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the disease transmission. The result of the sensitivity analysis shows that the most sensitive parameter is β (Human-to-human transmission rate), followed by Λ (Human recruitment rate). Also, the result shows that increase in ψ (compliance rate to particulate respirator by healthcare workers) leads to decrease in Ro which reduces tuberculosis spread among healthcare workers.

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.

Mathematical modeling of the impact of temperature variations and immigration on malaria prevalence in Nigeria

2021 ◽  
pp. 2150067
Author(s):  
Eunice E. Ukwajunor ◽  
Eno E. E. Akarawak ◽  
Israel Olutunji Abiala
Keyword(s):  
Equilibrium Point ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Malaria Incidence ◽  
Malaria Prevalence ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Marginal Effect ◽  
Asymptotically Stable ◽  
The Impact

The study examines the population-level impact of temperature variability and immigration on malaria prevalence in Nigeria, using a novel deterministic model. The model incorporates disease transmission by immigrants into the community. In the absence of immigration, the model is shown to exhibit the phenomenon of backward bifurcation. The disease-free equilibrium of the autonomous version of the model was found to be locally asymptotically stable in the absence of infective immigrants. However, the model exhibits an endemic equilibrium point when the immigration parameter is greater than zero. The endemic equilibrium point is seen to be globally asymptotically stable in the absence of disease-induced mortality. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to malaria transmission dynamics in Nigeria, shows that the top three parameters that drive malaria prevalence (with respect to [Formula: see text]) are the mosquito natural death rate ([Formula: see text]), mosquito biting rate ([Formula: see text]) and the transmission rates between humans and mosquitoes ([Formula: see text]). Numerical simulations of the model show that in Nigeria, malaria burden increases with increasing mean monthly temperature in the range of 22–28[Formula: see text]. Thus, this study suggests that control strategies for malaria should be intensified during this period. It is further shown that the proportion of infective immigrants has marginal effect on the transmission dynamics of the disease. Therefore, the simulations suggest that a reduction in the fraction of infective immigrants, either exposed or infectious, would significantly reduce the malaria incidence in a population.

scholarly journals Parameter Dependencies of a Biomechanical Cervical Spine FSU - The Process of Finding Optimal Model Parameters by Sensitivity Analysis

2021 ◽  
Author(s):  
Sabine Bauer ◽  
Ivanna Kramer
Keyword(s):  
Sensitivity Analysis ◽  
Intervertebral Discs ◽  
Model Parameters ◽  
Biomechanical Behavior ◽  
Functional Spinal Unit ◽  
Spine Model ◽  
Biomechanical Parameters ◽  
Multi Body ◽  
The Impact

The knowledge about the impact of structure-specific parameters on the biomechanical behavior of a computer model has an essential meaning for the realistic modeling and system improving. Especially the biomechanical parameters of the intervertebral discs, the ligamentous structures and the facet joints are seen in the literature as significant components of a spine model, which define the quality of the model. Therefore, it is important to understand how the variations of input parameters for these components affect the entire model and its individual structures. Sensitivity analysis can be used to gain the required knowledge about the correlation of the input and output variables in a complex spinal model. The present study analyses the influence of the biomechanical parameters of the intervertebral disc using different sensitivity analysis methods to optimize the spine model parameters. The analysis is performed with a multi-body simulation model of the cervical functional spinal unit C6-C7.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

scholarly journals A physically-based parsimonious hydrological model for flash floods in Mediterranean catchments

2011 ◽  
Vol 11 (9) ◽  
pp. 2567-2582 ◽  
Author(s):  
H. Roux ◽  
D. Labat ◽  
P.-A. Garambois ◽  
M.-M. Maubourguet ◽  
J. Chorda ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Soil Properties ◽  
Overland Flow ◽  
Hydrological Model ◽  
Extreme Event ◽  
Model Parameters ◽  
Peak Time ◽  
Efficiency Coefficient ◽  
Soil Saturation ◽  
The Impact

Abstract. A spatially distributed hydrological model, dedicated to flood simulation, is developed on the basis of physical process representation (infiltration, overland flow, channel routing). Estimation of model parameters requires data concerning topography, soil properties, vegetation and land use. Four parameters are calibrated for the entire catchment using one flood event. Model sensitivity to individual parameters is assessed using Monte-Carlo simulations. Results of this sensitivity analysis with a criterion based on the Nash efficiency coefficient and the error of peak time and runoff are used to calibrate the model. This procedure is tested on the Gardon d'Anduze catchment, located in the Mediterranean zone of southern France. A first validation is conducted using three flood events with different hydrometeorological characteristics. This sensitivity analysis along with validation tests illustrates the predictive capability of the model and points out the possible improvements on the model's structure and parameterization for flash flood forecasting, especially in ungauged basins. Concerning the model structure, results show that water transfer through the subsurface zone also contributes to the hydrograph response to an extreme event, especially during the recession period. Maps of soil saturation emphasize the impact of rainfall and soil properties variability on these dynamics. Adding a subsurface flow component in the simulation also greatly impacts the spatial distribution of soil saturation and shows the importance of the drainage network. Measures of such distributed variables would help discriminating between different possible model structures.

scholarly journals A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

2020 ◽  
Vol 24 (5) ◽  
pp. 917-922
Author(s):  
J. Andrawus ◽  
F.Y. Eguda ◽  
I.G. Usman ◽  
S.I. Maiwa ◽  
I.M. Dibal ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Line Treatment ◽  
Second Line ◽  
Tuberculosis Transmission ◽  
Disease Free

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

scholarly journals The effect of heterogeneous infectious period and contagiousness on the dynamics ofSalmonellatransmission in dairy cattle

2008 ◽  
Vol 136 (11) ◽  
pp. 1496-1510 ◽  
Author(s):  
C. LANZAS ◽  
S. BRIEN ◽  
R. IVANEK ◽  
Y. LO ◽  
P. P. CHAPAGAIN ◽  
...  
Keyword(s):  
Dairy Cattle ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Infectious Period ◽  
Specific Group ◽  
Infection Transmission ◽  
Force Of Infection ◽  
The Impact

SUMMARYThe objective of this study was to address the impact of heterogeneity of infectious period and contagiousness onSalmonellatransmission dynamics in dairy cattle populations. We developed three deterministic SIR-type models with two basic infected stages (clinically and subclinically infected). In addition, model 2 included long-term shedders, which were defined as individuals with low contagiousness but long infectious period, and model 3 included super-shedders (individuals with high contagiousness and long infectious period). The simulated dynamics, basic reproduction number (R0) and critical vaccination threshold were studied. Clinically infected individuals were the main force of infection transmission for models 1 and 2. Long-term shedders had a small impact on the transmission of the infection and on the estimated vaccination thresholds. The presence of super-shedders increasesR0and decreases the effectiveness of population-wise strategies to reduce infection, making necessary the application of strategies that target this specific group.

Sensitivity analysis of an integrated numerical flow model output to key parameters used in common qualitative vulnerability assessment methods

2020 ◽  
Author(s):  
Joanna Doummar ◽  
Assaad H. Kassem
Keyword(s):  
Sensitivity Analysis ◽  
Vulnerability Assessment ◽  
Groundwater Vulnerability ◽  
Assessment Methods ◽  
Qualitative Assessment ◽  
Model Parameters ◽  
Karst Aquifers ◽  
Model Output ◽  
Local Sensitivity ◽  
The Impact

&lt;p&gt;Qualitative vulnerability assessment methods applied in karst aquifers rely on key factors in the hydrological compartments usually assigned different weights according to their estimated impact on groundwater vulnerability. Based on an integrated numerical groundwater model on a snow-governed karst catchment area (Assal Spring- Lebanon), the aim of this work is to quantify the importance of the most influential parameters on recharge and spring discharge and outline potential parameters that are not accounted for in standard methods, when in fact they do play a role in the intrinsic vulnerability of a system. The assessment of the model sensitivity and the ranking of parameters are conducted using an automatic calibration tool for local sensitivity analysis in addition to a variance-based local sensitivity assessment of model output time series (recharge and discharge) &amp;#160;for two consecutive years (2016-2017) to various model parameters. The impact of each parameter was normalized to estimate standardized weights for each of the process based key-controlling parameters. Parameters to which model was sensitive were factors related to soil, 2) fast infiltration (bypass function) typical of karst aquifers, 3) climatic parameters (melting temperature and degree day coefficient) and 4) aquifer hydraulic properties that play a major role in groundwater vulnerability inducing a temporal effect and varied recession. Other less important parameters play different roles according to different assigned weights proportional to their ranking. Additionally, the effect of slope/geomorphology (e.g., dolines) was further investigated. &amp;#160;In general, this study shows that the weighting coefficients assigned to key vulnerability factors in the qualitative assessment methods can be reevaluated based on this process-based approach.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

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. 

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