Parameter estimation, sensitivity and control strategies analysis in the spread of influenza in Mexico

Prieto, Kernel; Ibargüen-Mondragón, Eduardo

doi:10.1088/1742-6596/1408/1/012020

Cited by 11 publications

(7 citation statements)

References 9 publications

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“…The sensitivity analysis is performed to determine which model parameters are the most important to disease transmission and prevalence (the parameters that are the most sensitive with respect to the initial transmission of the disease). In this study, we use it to discover parameters that have a high impact on reproduction number, and should be targeted by intervention strategies [26]. If a variable is a differentiable function of the parameter, the sensitivity indices may be alternatively defined using partial derivatives [25].…”

Section: Global Stability Of the Endemic Equilibriummentioning

confidence: 99%

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Liana,

Swai

2024

Abstract and Applied Analysis

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Coccidiosis is an infectious disease caused by the Eimeria species. The species can infect a bird’s digestive system, severely slow down its growth, and is a serious economic burden for chickens. A mathematical model for the transmission dynamics of coccidiosis disease in chickens in the presence of control interventions has been formulated and analyzed to gain insights into the dynamics of the disease in the population. Three control interventions, namely vaccination, sanitation, and treatment, are implemented. The study intends to assess the effects of these control interventions in coccidiosis transmission dynamics. Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. Analytical methods are employed to establish equilibrium solutions and investigate the stability of the model system’s equilibria, while numerical simulations illustrate the analytical results. The effective reproduction number is obtained using the next-generation matrix method, and the local stability of the equilibria of the model is established. The disease-free equilibrium is proved to be locally stable when the effective reproduction number is less than unity. Also, the nature of the bifurcation and its implications for disease prevention are investigated through the application of the center manifold theory. On the other hand, sensitivity analysis is carried out to investigate the parameters that impact the transmission of coccidiosis disease using the normalized forward sensitivity index. The parameters that have a greater influence on the effective reproduction number should be targeted for control purposes to lessen the spread of disease. Furthermore, numerical simulation is performed to investigate the contribution of each control intervention.

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Section: Global Stability Of the Endemic Equilibriummentioning

confidence: 99%

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Liana,

Swai

2024

Abstract and Applied Analysis

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“…The fitting curve or estimation of the parameters of a model is considered to be an inverse problem from the mathematical point of view. Typically, an optimisation method such as the Landweber in [49][50][51][52][53], or faster methods such as the Levenberg-Marquardt or Conjugate Gradient methods, and regularisation techniques, such as Tikhonov, Sparsity or Total Variation are used to solve this inverse problem. In this manuscript, I used Bayesian inference to solve the inverse problem because it is a tool that combines uncertainty propagation of measured data with available prior information of the model's parameters.…”

Section: Plos Onementioning

confidence: 99%

Current forecast of COVID-19 in Mexico: A Bayesian and machine learning approaches

Prieto

2022

PLoS ONE

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The COVID-19 pandemic has been widely spread and affected millions of people and caused hundreds of deaths worldwide, especially in patients with comorbilities and COVID-19. This manuscript aims to present models to predict, firstly, the number of coronavirus cases and secondly, the hospital care demand and mortality based on COVID-19 patients who have been diagnosed with other diseases. For the first part, I present a projection of the spread of coronavirus in Mexico, which is based on a contact tracing model using Bayesian inference. I investigate the health profile of individuals diagnosed with coronavirus to predict their type of patient care (inpatient or outpatient) and survival. Specifically, I analyze the comorbidity associated with coronavirus using Machine Learning. I have implemented two classifiers: I use the first classifier to predict the type of care procedure that a person diagnosed with coronavirus presenting chronic diseases will obtain (i.e. outpatient or hospitalised), in this way I estimate the hospital care demand; I use the second classifier to predict the survival or mortality of the patient (i.e. survived or deceased). I present two techniques to deal with these kinds of unbalanced datasets related to outpatient/hospitalised and survived/deceased cases (which occur in general for these types of coronavirus datasets) to obtain a better performance for the classification.

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“…2 ; ð3Þ such that x = F(θ) holds, with y obs is the observable data which has error measurements of size η. Problem (3) may be solved using numerical tools to deal with a non-linear least-squares problem [54][55][56][57][58]. In this work, we implement Bayesian inference to solve the inverse problem…”

Section: Parameter Estimationmentioning

confidence: 99%

On mobility trends analysis of COVID–19 dissemination in Mexico City

2022

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This work presents a tool for forecasting the spread of the new coronavirus in Mexico City, which is based on a mathematical model with a metapopulation structure that uses Bayesian statistics and is inspired by a data-driven approach. The daily mobility of people in Mexico City is mathematically represented by an origin-destination matrix using the open mobility data from Google and the Transportation Mexican Survey. This matrix is incorporated in a compartmental model. We calibrate the model against borough-level incidence data collected between 27 February 2020 and 27 October 2020, while using Bayesian inference to estimate critical epidemiological characteristics associated with the coronavirus spread. Given that working with metapopulation models leads to rather high computational time consumption, and parameter estimation of these models may lead to high memory RAM consumption, we do a clustering analysis that is based on mobility trends to work on these clusters of borough separately instead of taken all of the boroughs together at once. This clustering analysis can be implemented in smaller or larger scales in different parts of the world. In addition, this clustering analysis is divided into the phases that the government of Mexico City has set up to restrict individual movement in the city. We also calculate the reproductive number in Mexico City using the next generation operator method and the inferred model parameters obtaining that this threshold is in the interval (1.2713, 1.3054). Our analysis of mobility trends can be helpful when making public health decisions.

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Parameter estimation, sensitivity and control strategies analysis in the spread of influenza in Mexico

Cited by 11 publications

References 9 publications

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Current forecast of COVID-19 in Mexico: A Bayesian and machine learning approaches

On mobility trends analysis of COVID–19 dissemination in Mexico City

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