Mathematical analysis on SEIR-type model of the Tuberculosis disease spread with vaccination and treatment elements

Ramli, Marwan; Zulfa, Syarifah Chaira; Chaniago, Natasya Ayuningtia; Halfiani, Vera

doi:10.1088/1742-6596/1235/1/012120

Cited by 8 publications

(3 citation statements)

References 3 publications

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“…We developed and validated single and multiple population ordinary differential equations (ODE) and agent-based models of COVID-19 spread within and between defined groups of individuals. The general model logic (Multimedia Appendix 1) was adapted from classic susceptible-exposed-infected-recovered (SEIR) frameworks [67,68] similar to those described elsewhere for many other infectious diseases [63][64][65][66][67][68][69][70][71][72][73][74][75][76]. The single population model describes spread dynamics within one defined population (eg, on-campus students or local community residents), whereas the multipopulation model additionally includes cross-exposure between two or more groups.…”

Section: Model Overviewmentioning

confidence: 99%

Community and Campus COVID-19 Risk Uncertainty Under University Reopening Scenarios: Model-Based Analysis

Benneyan¹,

Gehrke²,

Ilieş³

et al. 2021

JMIR Public Health Surveill

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Background Significant uncertainty has existed about the safety of reopening college and university campuses before the COVID-19 pandemic is better controlled. Moreover, little is known about the effects that on-campus students may have on local higher-risk communities. Objective We aimed to estimate the range of potential community and campus COVID-19 exposures, infections, and mortality under various university reopening plans and uncertainties. Methods We developed campus-only, community-only, and campus × community epidemic differential equations and agent-based models, with inputs estimated via published and grey literature, expert opinion, and parameter search algorithms. Campus opening plans (spanning fully open, hybrid, and fully virtual approaches) were identified from websites and publications. Additional student and community exposures, infections, and mortality over 16-week semesters were estimated under each scenario, with 10% trimmed medians, standard deviations, and probability intervals computed to omit extreme outliers. Sensitivity analyses were conducted to inform potential effective interventions. Results Predicted 16-week campus and additional community exposures, infections, and mortality for the base case with no precautions (or negligible compliance) varied significantly from their medians (4- to 10-fold). Over 5% of on-campus students were infected after a mean of 76 (SD 17) days, with the greatest increase (first inflection point) occurring on average on day 84 (SD 10.2 days) of the semester and with total additional community exposures, infections, and mortality ranging from 1-187, 13-820, and 1-21 per 10,000 residents, respectively. Reopening precautions reduced infections by 24%-26% and mortality by 36%-50% in both populations. Beyond campus and community reproductive numbers, sensitivity analysis indicated no dominant factors that interventions could primarily target to reduce the magnitude and variability in outcomes, suggesting the importance of comprehensive public health measures and surveillance. Conclusions Community and campus COVID-19 exposures, infections, and mortality resulting from reopening campuses are highly unpredictable regardless of precautions. Public health implications include the need for effective surveillance and flexible campus operations.

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Section: Model Overviewmentioning

confidence: 99%

Community and Campus COVID-19 Risk Uncertainty Under University Reopening Scenarios: Model-Based Analysis

Benneyan¹,

Gehrke²,

Ilieş³

et al. 2021

JMIR Public Health Surveill

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“…We developed and validated mathematical epidemiology single and multiple population models of the spread of Covid-19 within and between defined groups of individuals, including standard ordinary different equation (ODE) and agent-based models. The general logic of each model was adapted from classic and well-accepted susceptible-exposed-infected-recovered (SEIR) frameworks 67,68 similar to those reported on elsewhere for HIV, 65 tuberculosis, 69,70 Zika, 71,72 Ebola, 73 drug abuse, [74][75][76] Covid-19, 66 and many other contagion or spread concerns 63,64 . The single population models describe spread dynamics within one defined population (e.g.…”

Section: A Model Development and Validationmentioning

confidence: 99%

Potential Community and Campus Covid-19 Outcomes Under University and College Reopening Scenarios

Benneyan

Gehrke

Ilieş

et al. 2020

Preprint

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Background: Significant uncertainty exists about the safety of, and best strategies for, reopening colleges and universities while the Covid-19 pandemic is not well-controlled. Little also is known about the effects that on-campus outbreaks may have on local non-student and/or higher-risk communities. Model-based analysis can help inform decision and policy making across a wide range of assumptions and uncertainties. Objective: To evaluate the potential range of campus and community Covid-19 exposures, infections, and mortality due to various university and college reopening plans and precautions. Methods: We developed and calibrated campus-only, community-only, and campus-x-community epidemic models using standard susceptible-exposed-infected-recovered differential equation and agent-based modeling methods. Input parameters for campus and surrounding communities were estimated via published and grey literature, scenario development, expert opinion, Monte Carlo simulation, and accuracy optimization algorithms; models were cross-validated against each other using February-June 2020 county, state, and country data. Campus opening plans (spanning various fully open, hybrid, and fully virtual approaches) were identified from websites, publications, communications, and surveys. All scenarios were simulated assuming 16-week semesters and best/worst case ranges for disease prevalence among community residents and arriving students, precaution compliance, contact frequency, virus attack rates, and tracing and isolation effectiveness. Day-to-day student and community differences in exposures, infections, and mortality were estimated under each scenario as compared to regular and no re-opening; 10% trimmed medians, standard deviations, and probability intervals were computed to omit extreme outlier scenarios. Factorial analyses were conducted to identify inputs with largest and smallest impacts on outcomes. Results: As a base case, predicted 16-week student infections and mortality under normal operations with no precautions (or no compliance) ranged from 472 to 9,484 (4.7% to 94.8%) and 2 to 61 (0.02% to 0.61%) per 10,000 student population, respectively. In terms of contact tracing and isolation resources, as many as 17 to 1,488 total exposures per 10,000 students could occur on a given day throughout the semester needing to be located, tested, and if warranted quarantined. Attributable total additional predicted community exposures, infections, and mortality ranged from 1 to 187, 13 to 820, and 1 to 21, respectively, assuming the university takes no additional precautions to limit exposure risk. The mean (SD) number of days until 1% and 5% of on-campus students are infected was 11 (3) and 76 (17) days, respectively; 34.8% of replications resulted in more than 10% students infected by semester end. The diffusion first inflection point occurred on average on day 84 (+/- 20 days, 95% interval). Common re-opening precaution strategies reduced the above consequences by 24% to 26% fewer infections (now 360 to 6,976 per 10,000 students) and 36% to 50% fewer deaths (now 1 to 39 per 10,000 students). Perfect testing and immediate quarantining of all students on arrival to campus at semester start further reduced infections by 58% to 95% (now 200 to 468 per 10,000 students) and deaths by 95% to 100% (now 0 to 3 per 10,000 students). Uncertainties in many factors, however, produced tremendous variability in all median estimates, ranging by -67% to +370%. Conclusions: Consequences of reopening college and university physical campuses on student and community Covid-19 exposures, infections, and mortality are very highly unpredictable, depending on a combination of random chance, controllable (e.g. physical layouts), and uncontrollable (e.g. human behavior) factors. Important implications at government and academic institution levels include clear needs for specific criteria to adapt campus operations mid-semester, methods to detect when this is necessary, and well-executed contingency plans for doing so.

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“…ere are several SEIR (susceptible-exposed-infectiousrecovered) models that study infectious diseases in general [5][6][7]; since the appearance of the virus, the SEIR models proposed aim to study the behavior of this epidemic [8].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of COVID-19 Epidemic Model of Type $S E I Q H R$ with Fractional Order

Beinane

Lemnaouar

Zine

et al. 2022

Mathematical Problems in Engineering

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In this article, we consider a fractional S E I R model, denoted by the S E I Q H R model, which aims to predict the outbreak of infectious diseases in general. In particular, we study the spread of COVID-19. The fractional order offers a flexible, appropriate, and reliable framework for pandemic growth characterization. Firstly, we analyze some elementary results of the model (boundedness and uniqueness of solutions). In addition, we establish certain conditions to ensure the local stability of the disease-free and endemic equilibrium points. Based on analytical and numerical results, we conclude that coronavirus infection (COVID-19) remains endemic, which requires long-term prevention and intervention strategies.

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Mathematical analysis on SEIR-type model of the Tuberculosis disease spread with vaccination and treatment elements

Cited by 8 publications

References 3 publications

Community and Campus COVID-19 Risk Uncertainty Under University Reopening Scenarios: Model-Based Analysis

Community and Campus COVID-19 Risk Uncertainty Under University Reopening Scenarios: Model-Based Analysis

Potential Community and Campus Covid-19 Outcomes Under University and College Reopening Scenarios

Stability Analysis of COVID-19 Epidemic Model of Type $S E I Q H R$ with Fractional Order

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Mathematical analysis on SEIR-type model of the Tuberculosis disease spread with vaccination and treatment elements

Cited by 8 publications

References 3 publications

Community and Campus COVID-19 Risk Uncertainty Under University Reopening Scenarios: Model-Based Analysis

Community and Campus COVID-19 Risk Uncertainty Under University Reopening Scenarios: Model-Based Analysis

Potential Community and Campus Covid-19 Outcomes Under University and College Reopening Scenarios

Stability Analysis of COVID-19 Epidemic Model of Type S E I Q H R with Fractional Order

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Product

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Stability Analysis of COVID-19 Epidemic Model of Type $S E I Q H R$ with Fractional Order