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Sensitivity and elasticity analysis of novel corona virus transmission model: A mathematical approach.

ABSTRACT: The deadly corona virus continues to pound the globe mercilessly compelling mathematical models and computational simulations which might prove effective tools to enable global efforts to estimate key transmission parameters involved in the system. We propose a mathematical model using a set of non-linear differential equations to account for the spread of the COVID-19 infection with special compartment class isolation or quarantine and estimate the model parameters by fitting the model with reported data of the ongoing pandemic situation in India. The basic reproduction number is defined and local stability analysis is carried out at each equilibrium point in terms of the reproduction number R0 . The model is fitted mathematically and makes the data India specific. Additionally, we examined sensitivity analysis of the model. These outcomes recommend how to control the spread of corona, keeping in mind contact and recovery rate. Also we have investigated the elasticity of the basic reproduction number as a measure of control parameters of the dynamical system. Numerical simulations were also done to show that the proposed model is valid for the type and spread of the outbreak which happened in India.

SUBMITTER: Das K

PROVIDER: S-EPMC7943394 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Sensitivity and elasticity analysis of novel corona virus transmission model: A mathematical approach.

Das Kalyan K Ranjith Kumar G G Madhusudhan Reddy K K Lakshminarayan K K

Sensors international 20210310

The deadly corona virus continues to pound the globe mercilessly compelling mathematical models and computational simulations which might prove effective tools to enable global efforts to estimate key transmission parameters involved in the system. We propose a mathematical model using a set of non-linear differential equations to account for the spread of the COVID-19 infection with special compartment class isolation or quarantine and estimate the model parameters by fitting the model with rep ...[more]

PMID: 34766050

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Project description:Epstein-Barr virus (EBV) establishes a lifelong latent infection in healthy humans, kept under immune control by cytotoxic T cells (CTLs). Following paediatric haematopoetic stem cell transplantation (HSCT), a loss of immune surveillance leads to opportunistic outgrowth of EBV-infected cells, resulting in EBV reactivation, which can ultimately progress to post-transplant lymphoproliferative disorder (PTLD). The aims of this study were to identify risk factors for EBV reactivation in children in the first 100 days post-HSCT and to assess the suitability of a previously reported mathematical model to mechanistically model EBV reactivation kinetics in this cohort. Retrospective electronic data were collected from 56 children who underwent HSCT at Great Ormond Street Hospital (GOSH) between 2005 and 2016. Using EBV viral load (VL) measurements from weekly quantitative PCR (qPCR) monitoring post-HSCT, a multivariable Cox proportional hazards (Cox-PH) model was developed to assess time to first EBV reactivation event in the first 100 days post-HSCT. Sensitivity analysis of a previously reported mathematical model was performed to identify key parameters affecting EBV VL. Cox-PH modelling revealed EBV seropositivity of the HSCT recipient and administration of anti-thymocyte globulin (ATG) pre-HSCT to be significantly associated with an increased risk of EBV reactivation in the first 100 days post-HSCT (adjusted hazard ratio (AHR) = 2.32, P = 0.02; AHR = 2.55, P = 0.04). Five parameters were found to affect EBV VL in sensitivity analysis of the previously reported mathematical model. In conclusion, we have assessed the effect of multiple covariates on EBV reactivation in the first 100 days post-HSCT in children and have identified key parameters in a previously reported mechanistic mathematical model that affect EBV VL. Future work will aim to fit this model to patient EBV VLs, develop the model to account for interindividual variability and model the effect of clinically relevant covariates such as rituximab therapy and ATG on EBV VL.

Project description:Quantitative models of gene expression generate parameter values that can shed light on biological features such as transcription factor activity, cooperativity, and local effects of repressors. An important element in such investigations is sensitivity analysis, which determines how strongly a model's output reacts to variations in parameter values. Parameters of low sensitivity may not be accurately estimated, leading to unwarranted conclusions. Low sensitivity may reflect the nature of the biological data, or it may be a result of the model structure. Here, we focus on the analysis of thermodynamic models, which have been used extensively to analyze gene transcription. Extracted parameter values have been interpreted biologically, but until now little attention has been given to parameter sensitivity in this context.We apply local and global sensitivity analyses to two recent transcriptional models to determine the sensitivity of individual parameters. We show that in one case, values for repressor efficiencies are very sensitive, while values for protein cooperativities are not, and provide insights on why these differential sensitivities stem from both biological effects and the structure of the applied models. In a second case, we demonstrate that parameters that were thought to prove the system's dependence on activator-activator cooperativity are relatively insensitive. We show that there are numerous parameter sets that do not satisfy the relationships proferred as the optimal solutions, indicating that structural differences between the two types of transcriptional enhancers analyzed may not be as simple as altered activator cooperativity.Our results emphasize the need for sensitivity analysis to examine model construction and forms of biological data used for modeling transcriptional processes, in order to determine the significance of estimated parameter values for thermodynamic models. Knowledge of parameter sensitivities can provide the necessary context to determine how modeling results should be interpreted in biological systems.

Project description:BackgroundA substantial scale-up in public health response is needed to control the unprecedented Ebola virus disease (EVD) epidemic in west Africa. Current international commitments seek to expand intervention capacity in three areas: new EVD treatment centres, case ascertainment through contact tracing, and household protective kit allocation. We aimed to assess how these interventions could be applied individually and in combination to avert future EVD cases and deaths.MethodsWe developed a transmission model of Ebola virus that we fitted to reported EVD cases and deaths in Montserrado County, Liberia. We used this model to assess the effectiveness of expanding EVD treatment centres, increasing case ascertainment, and allocating protective kits for controlling the outbreak in Montserrado. We varied the efficacy of protective kits from 10% to 50%. We compared intervention initiation on Oct 15, 2014, Oct 31, 2014, and Nov 15, 2014. The status quo intervention was defined in terms of case ascertainment and capacity of EVD treatment centres on Sept 23, 2014, and all behaviour and contact patterns relevant to transmission as they were occurring at that time. The primary outcome measure was the expected number of cases averted by Dec 15, 2014.FindingsWe estimated the basic reproductive number for EVD in Montserrado to be 2·49 (95% CI 2·38-2·60). We expect that allocating 4800 additional beds at EVD treatment centres and increasing case ascertainment five-fold in November, 2014, can avert 77 312 (95% CI 68 400-85 870) cases of EVD relative to the status quo by Dec 15, 2014. Complementing these measures with protective kit allocation raises the expectation as high as 97 940 (90 096-105 606) EVD cases. If deployed by Oct 15, 2014, equivalent interventions would have been expected to avert 137 432 (129 736-145 874) cases of EVD. If delayed to Nov 15, 2014, we expect the interventions will at best avert 53 957 (46 963-60 490) EVD cases.InterpretationThe number of beds at EVD treatment centres needed to effectively control EVD in Montserrado substantially exceeds the 1700 pledged by the USA to west Africa. Accelerated case ascertainment is needed to maximise effectiveness of expanding the capacity of EVD treatment centres. Distributing protective kits can further augment prevention of EVD, but it is not an adequate stand-alone measure for controlling the outbreak. Our findings highlight the rapidly closing window of opportunity for controlling the outbreak and averting a catastrophic toll of EVD cases and deaths.FundingUS National Institutes of Health.

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Sensitivity and elasticity analysis of novel corona virus transmission model: A mathematical approach.

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Sensitivity and elasticity analysis of novel corona virus transmission model: A mathematical approach.

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