scholarly journals Sensitivity Analysis in a Dengue Epidemiological Model

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Helena Sofia Rodrigues ◽  
M. Teresa T. Monteiro ◽  
Delfim F. M. Torres
Keyword(s):  
Sensitivity Analysis ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Epidemiological Model ◽  
Model Parameters ◽  
Epidemiological Models ◽  
Dengue Disease ◽  
Health Practitioners ◽  
Public Health Practitioners ◽  
Entomological Data

Epidemiological models may give some basic guidelines for public health practitioners, allowing the analysis of issues that can influence the strategies to prevent and fight a disease. To be used in decision making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. Here an SIR (S for susceptible, I for infectious, and R for recovered individuals) and ASI (A for the aquatic phase of the mosquito, S for susceptible, and I for infectious mosquitoes) epidemiological model describing a dengue disease is presented, as well as the associated basic reproduction number. A sensitivity analysis of the epidemiological model is performed in order to determine the relative importance of the model parameters to the disease transmission.

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 Investigating the Role of Environmental Transmission in COVID-19 Dynamics: A Mathematical Model Based Study

2020 ◽  
Author(s):  
Ibrahim M. ELmojtaba ◽  
Fatma Al-Musalhi ◽  
Asma Al-Ghassani ◽  
Nasser Al-Salti
Keyword(s):  
Mathematical Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Model Parameters ◽  
Environmental Transmission ◽  
Estimated Parameters ◽  
Existence And Stability

Abstract A mathematical model with environmental transmission has been proposed and analyzed to investigate its role in the transmission dynamics of the ongoing COVID-19 outbreak. Two expressions for the basic reproduction number R0 have been analytically derived using the next generation matrix method. The two expressions composed of a combination of two terms related to human to human and environment to human transmissions. The value of R0 has been calculated using estimated parameters corresponding to two datasets. Sensitivity analysis of the reproduction number to the corresponding model parameters has been carried out. Existence and stability analysis of disease free and endemic equilibrium points have been presented in relation with the obtained expressions of R0. Numerical simulations to demonstrate the effect of some model parameters related to environmental transmission on the disease transmission dynamics have been carried out and the results have been demonstrated graphically.

scholarly journals An SEIARD epidemic model for COVID-19 in Mexico: mathematical analysis and state-level forecast

2020 ◽  
Author(s):  
Ugo Avila-Ponce de León ◽  
Ángel G. C. Pérez ◽  
Eric Avila-Vales
Keyword(s):  
Disease Transmission ◽  
Local Stability ◽  
Reproduction Number ◽  
State Level ◽  
Model Parameters ◽  
Relative Importance ◽  
Current Outbreak ◽  
Sensibility Analysis ◽  
Next Generation Matrix ◽  
Disease Free

We propose an SEIARD mathematical model to investigate the current outbreak of coronavirus disease (COVID-19) in Mexico. Our model incorporates the asymptomatic infected individuals, who represent the majority of the infected population (with symptoms or not) and could play an important role in spreading the virus without any knowledge. We calculate the basic reproduction number (R0) via the next-generation matrix method and estimate the per day infection, death and recovery rates. The local stability of the disease free equilibrium is established in terms of R0. A sensibility analysis is performed to determine the relative importance of the model parameters to the disease transmission. We calibrate the parameters of the SEIARD model to the reported number of infected cases and fatalities for several states in Mexico by minimizing the sum of squared errors and attempt to forecast the evolution of the outbreak until August 2020.

scholarly journals A Mathematical Model of COVID-19 with Vaccination and Treatment

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
M. L. Diagne ◽  
H. Rwezaura ◽  
S. Y. Tchoumi ◽  
J. M. Tchuenche
Keyword(s):  
Public Health ◽  
Mathematical Model ◽  
Disease Transmission ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
Public Health Intervention ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Model Parameters

We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures—vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number R 0 v is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever R 0 v > 1 , even if vaccine coverage is high. Pontryagin’s maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number R 0 = 1.31 at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when R 0 v > 1 , additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate b , the vaccine efficacy ε , the vaccination rate v , the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes σ and ϕ are the most impactful parameters.

scholarly journals Analysis of a model for waterborne diseases with Allee effect on bacteria

2020 ◽  
Vol 25 (6) ◽  
pp. 1035-1058
Author(s):  
Florinda Capone ◽  
Maria Francesca Carfora ◽  
Roberta De Luca ◽  
Isabella Torcicollo
Keyword(s):  
Sensitivity Analysis ◽  
Disease Transmission ◽  
Allee Effect ◽  
Causes Of Death ◽  
Reproduction Number ◽  
Hopf Bifurcations ◽  
Waterborne Diseases ◽  
Indirect Transmission ◽  
Existence And Stability ◽  
The Basic Reproduction Number

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown.

scholarly journals Modeling the transmission dynamics of tuberculosis in Khyber Pakhtunkhwa Pakistan

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985483 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Manzoor Ahmad ◽  
Saif Ullah ◽  
Muhammad Farooq ◽  
Taza Gul
Keyword(s):  
Sensitivity Analysis ◽  
Disease Transmission ◽  
Transmission Rate ◽  
Model Parameters ◽  
Bacterial Disease ◽  
Treatment Rate ◽  
Khyber Pakhtunkhwa ◽  
Infected People ◽  
Tuberculosis Transmission ◽  
Number Formula

This article addresses the dynamics of the bacterial disease tuberculosis in Khyber Pakhtunkhwa, Pakistan, through a mathematical model. In this work, the latent compartment is divided into slow and fast kinds of progresses. The model is parameterized based on the reported tuberculosis-infected cases in Khyber Pakhtunkhwa for the period 2002–2017. We obtain the basic reproduction number [Formula: see text] of the model using the next-generation method. The estimated value of [Formula: see text] for the given period is approximately 1.38. Furthermore, it is shown that the model has two types of equilibria: disease-free and endemic equilibriums. The global stability analysis of the model equilibria is shown via Lyapunov functions. We also perform the sensitivity analysis of [Formula: see text] and present their corresponding graphical results to examine the relative importance of various model parameters to tuberculosis transmission and prevalence. Finally, some numerical simulations are done for the estimated parameters and the key parameters effects are considered on the curtailing tuberculosis disease. From the numerical results and model sensitivity analysis, it is found that the spread of tuberculosis can be minimized by increasing the treatment rate [Formula: see text] of infected people and decreasing the effective disease transmission rate [Formula: see text] and the rate [Formula: see text] at which the individuals leave treated class reenter infected classes.

scholarly journals A Dynamic Model of Human and Livestock Tuberculosis Spread and Control in Urumqi, Xinjiang, China

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Shan Liu ◽  
Aiqiao Li ◽  
Xiaomei Feng ◽  
Xueliang Zhang ◽  
Kai Wang
Keyword(s):  
Sensitivity Analysis ◽  
Confidence Interval ◽  
Dynamic Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Parameters ◽  
Epidemiological Investigation ◽  
Dynamical Behaviors ◽  
And Control ◽  
The Basic Reproduction Number

We establish a dynamical model for tuberculosis of humans and cows. For the model, we firstly give the basic reproduction numberR0. Furthermore, we discuss the dynamical behaviors of the model. By epidemiological investigation of tuberculosis among humans and livestock from 2007 to 2014 in Urumqi, Xinjiang, China, we estimate the parameters of the model and study the transmission trend of the disease in Urumqi, Xinjiang, China. The reproduction number in Urumqi for the model is estimated to be 0.1811 (95% confidence interval: 0.123–0.281). Finally, we perform some sensitivity analysis of several model parameters and give some useful comments on controlling the transmission of tuberculosis.

scholarly journals African Trypanosomiasis Dynamics: Modelling the Effects of Treatment, Education, and Vector Trapping

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yustina A. Liana ◽  
Nyimvua Shaban ◽  
Goodluck Mlay ◽  
Anitha Phibert
Keyword(s):  
Disease Transmission ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Public Health Education ◽  
Tsetse Fly ◽  
Control Measures ◽  
Effective Control ◽  
Tsetse Flies ◽  
Model Parameters ◽  
African Trypanosomiasis

African trypanosomiasis is a vector-borne disease that is mainly transmitted by infected tsetse flies. A deterministic model of tsetse fly vector, human, and cattle hosts is formulated and analyzed to gain insights into the disease dynamics. The roles of public health education, treatment, and tsetse fly traps are studied. The effective reproduction number, a threshold used to determine whether the disease persists or dies out in the population, is determined. The sensitivity analysis of the model parameters is performed to determine their relationship with the effective reproduction number. The results show that the tsetse fly biting rate is the most sensitive parameter to the effective reproduction number. Furthermore, the model’s numerical simulation shows that a combination of all three interventions has the most significant impact on the control of African trypanosomiasis. Thus, we recommend that these control measures be put concurrently in endemic areas for effective control of the disease transmission.

scholarly journals A Model for the Testing and Tracing Needed to Suppress COVID-19

2020 ◽  
Author(s):  
Victor Wang
Keyword(s):  
Reproduction Number ◽  
Infectious Period ◽  
Simple Mathematical Model ◽  
Susceptible Population ◽  
Seir Model ◽  
Social Distancing ◽  
Health Practitioners ◽  
Public Health Practitioners ◽  
The Basic Reproduction Number ◽  
Close Contacts

AbstractThis paper presents a simple mathematical model that answers how much testing and tracing we need to do to suppress new surges of COVID-19 infections after reopening. We derived the model by modifying the SEIR model taking into the effects of testing and tracing. The following equation is one of the essential outcomes of the model: Where ρ is the percentage of infectious people that have to be detected per day, R0 is the basic reproduction number, S/N is the percentage of the susceptible population over the entire population, D is the length of the infectious period, and η is the percentage of close contacts that have to be traced. If the above equation is satisfied, we can bring the effective reproduction number Re to below 1 to get the transmission suppressed. This model demonstrates that together with social-distancing measures such as wearing masks in public, with a reasonable amount of testing and tracing, we may suppress the COVID-19 transmission for good. For example, if social distancing measures can bring R0 to below 1.2, for D being 10 days, in places where 15% people have developed antibodies, we can suppress the transmission by detecting only 0.13% of the infectious population daily while tracing 50% of their close contacts. The model provides intuitive insights and quantitative guidance for policymakers and public health practitioners to deploy the testing and tracing resources optimally.

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