scholarly journals Stability and global sensitivity analysis of the transmission dynamics of malaria with relapse and ignorant infected humans

2022 ◽  
Author(s):  
Yves Tinda Mangongo ◽  
Joseph-Désiré Kyemba Bukweli ◽  
Justin Dupar Busili Kampempe ◽  
Rostin Matendo Mabela ◽  
Justin Manango Wazute Munganga
Keyword(s):  
Sensitivity Analysis ◽  
Recovery Rate ◽  
Global Sensitivity Analysis ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Sensitivity ◽  
Partial Rank Correlation

Abstract In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.

scholarly journals Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Sara Bidah ◽  
Omar Zakary ◽  
Mostafa Rachik
Keyword(s):  
Sensitivity Analysis ◽  
Correlation Coefficient ◽  
Global Sensitivity Analysis ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Latin Hypercube ◽  
Global Sensitivity ◽  
Existence And Stability ◽  
Partial Rank Correlation

In this paper, we present a new mathematical model that describes agree-disagree opinions during polls. We first present the model and its different compartments. Then, we use the next-generation matrix method to compute thresholds of equilibrium stability. We perform the stability analysis of equilibria to determine under which conditions these equilibrium points are stable or unstable. We show that the existence and stability of these equilibria are controlled by the calculated thresholds. Finally, we also perform several computational and statistical experiments to validate the theoretical results obtained in this work. To study the influence of various parameters on these thresholds and to identify the most influential parameters, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling.

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 The trade-off between mobility and vaccination for COVID-19 control: a metapopulation modeling approach

2020 ◽  
Author(s):  
Fernando Saldana ◽  
Jorge X. Velasco-Hernandez
Keyword(s):  
Sensitivity Analysis ◽  
Epidemic Model ◽  
Global Sensitivity Analysis ◽  
Immunization Coverage ◽  
Transmission Dynamics ◽  
Percentage Reduction ◽  
Delivery Time ◽  
Trade Off ◽  
Global Sensitivity ◽  
Safe Vaccine

November 2020 received a string of encouraging results from leading vaccine developers raising hopes for the imminent availability of an effective and safe vaccine against the SARS-CoV-2. In the present work, we discuss the theoretical impact of introducing a vaccine across a range of scenarios . In particular, we investigate how vaccination coverage, efficacy, and delivery time affect the control of the transmission dynamics in comparison to mobility restrictions. The analysis is based on a metapopulation epidemic model structured by risk. We perform a global sensitivity analysis using the Sobol method. Our analysis suggest that the reduction of mobility among patches play a significant role in the mitigation of the disease close to the effect of immunization coverage of 30\% achieved in 4 months. Moreover, for an immunization coverage between 20\%-50\% achieved in the first half of 2021 with a vaccine efficacy between 70\%-95\%, the percentage reduction in the total number of SARS-CoV-2 infections is between 30\%-50\% by the end of 2021 in comparison with the no vaccination scenario.

scholarly journals GLOBAL SENSITIVITY ANALYSIS FOR TRANSFORMATION OF HOEK-BROWN FAILURE CRITERION FOR ROCK MASS

2018 ◽  
Vol 24 (5) ◽  
pp. 390-398 ◽  
Author(s):  
Jan Štefaňák ◽  
Zdeněk Kala ◽  
Lumír Miča ◽  
Arnoldas Norkus
Keyword(s):  
Sensitivity Analysis ◽  
Failure Criterion ◽  
Global Sensitivity Analysis ◽  
Latin Hypercube Sampling ◽  
Strength Criterion ◽  
Jointed Rock ◽  
Rock Massif ◽  
Order Effects ◽  
Statistical Parameters ◽  
Global Sensitivity

A variety of engineering activities require reliable evaluation of rock strength. For instance, the stability of rock slopes depends on structural geology of rock massif in which the slope is excavated. Hoek-Brown (HB) failure criterion applied in rock design practice introduces factors based on the properties of jointed rock. The non-linear finite element safety calculation is conveniently used for calculation safety the factor of slope stability. The Mohr-Coulomb (MC) failure (strength) criterion for soil is widely applied in geotechnical design. Therefore, the appropriate transformation from HB to the equivalent MC, employing angle of shearing resistance φ and cohesion c, is necessary. This article studies the effect of jointed rock massif properties on the transformed MC parameters by using Sobol’s global sensitivity analysis (SSA) and HB transformation equations. Statistical parameters needed for the evaluation of sensitivity analysis are processed using classical statistical methods upon the emulation of Latin Hypercube Sampling simulation methods. Developed and adapted by authors techniques are illustrated by processing real rock investigation data from survey of the trachyte massif located in the Czech Republic. The first and higher order effects of random inputs are identified using SSA. It is illustrated that the effects of inputs on the MC parameters varies significantly depending on the discontinuity distribution and height of the slope.

Sign in / Sign up

Export Citation Format

Share Document