A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations

Gumel, Abba B.; Iboi, Enahoro; Ngonghala, Calistus N.; Elbasha, Elamin H.

doi:10.1016/j.idm.2020.11.005

Cited by 133 publications

(133 citation statements)

References 40 publications

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“…Depending on the situation, the geometrical approach involves comparing the slopes of the curves given by equations (8)- (11). We consider the following two scenarios, based on which group(s) the vaccine is prioritized to.…”

Section: Herd Immunity Thresholds For a Two-group Model With Heterogementioning

confidence: 99%

“…When the absolute value of the slope of the blue line (equation (11)) is between the absolute values of the slope of the orange curve when it intersects the y-axis (equation (9)) and x-axis (equation (10)), it is optimal to vaccinate both groups (illustrated in Figure 1c). The interior solution is obtained when the slope of the orange curve (equation (8)) is equal to the slope of the blue curve (equation (11)). Thus, by equating the right-hand side of equations (8) and (11) and solving for 1 * and using the resulting solution in equations (6), we have:…”

Section: Scenario 2: Vaccinating Both Groupsmentioning

confidence: 99%

“…The interior solution is obtained when the slope of the orange curve (equation (8)) is equal to the slope of the blue curve (equation (11)). Thus, by equating the right-hand side of equations (8) and (11) and solving for 1 * and using the resulting solution in equations (6), we have:…”

Section: Scenario 2: Vaccinating Both Groupsmentioning

confidence: 99%

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Vaccination and herd immunity thresholds in heterogeneous populations

Elbasha

Gumel

2021

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It has been suggested, without rigorous mathematical analysis, that the classical vaccine-induced herd immunity threshold (HIT) assuming a homogeneous population can be substantially higher than the minimum HIT obtained when considering population heterogeneities. We investigated this claim by developing, and rigorously analyzing, a vaccination model that incorporates various forms of heterogeneity and compared it with a model of a homogeneous population. By employing a two-group vaccination model in heterogeneous populations, we theoretically established conditions under which heterogeneity leads to different HIT values, depending on the relative values of the contact rates for each group, the type of mixing between groups, relative vaccine efficacy, and the relative population size of each group. For example, under biased random mixing and when vaccinating a given group results in disproportionate prevention of higher transmission per capita, it is optimal to vaccinate that group before vaccinating other groups. We also found situations, under biased assortative mixing assumption, where it is optimal to vaccinate more than one group. We show that regardless of the form of mixing between groups, the HIT values assuming a heterogeneous population are always lower than the HIT values obtained from a corresponding model with a homogeneous population. Using realistic numerical examples and parametrization (e.g., assuming assortative mixing together with vaccine efficacy of 95% and basic reproduction number of 2.5), we demonstrate that the HIT value considering heterogeneity (e.g., biased assortative mixing) is significantly lower (40%) compared with a HIT value of (63%) assuming a homogeneous population.

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Section: Herd Immunity Thresholds For a Two-group Model With Heterogementioning

confidence: 99%

Section: Scenario 2: Vaccinating Both Groupsmentioning

confidence: 99%

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Vaccination and herd immunity thresholds in heterogeneous populations

Elbasha

Gumel

2021

Preprint

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“…In terms of vaccination models for COVID- 19 pandemic, the number of studies is quite limited compared to modeling of non-pharmacologic interventions. For example, Gumel et al present a model by decomposing susceptible compartment as vaccinated and unvaccinated sub-classes by discussing stability and threshold for herd immunity [21]. In another study [22], a heterogeneous model based on the face mask use is presented and success of vaccination together with social-distancing is discussed.…”

Section: Introductionmentioning

confidence: 99%

Assessment of Vaccination and Underreporting on COVID-19 Infections in Turkey Based On Effective Reproduction Number

Kose

Tuncer

2021

Preprint

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In this paper, we introduce a SEIR type COVID-19 model where the infected class is further divided into individuals in intensive care (ICUs) and ventilation units. The model is validated with the COVID-19 cases, deaths, and the number of patients in ICUs and ventilation units as reported by Turkey Department of Health for the period March 11 through May 30 when the nationwide lockdown is in order. COVID-19 interventions in Turkey are incorporated into the model to detect the future trend of the outbreak accurately. The lockdown is lifted on June 1, and the model is modified to include a time dependent transmission rate which is linked to the effective reproduction number Rt through basic reproduction number R0. The modified model captures the changing dynamics and peaks of the outbreak successfully. With the onset of vaccination on 13 January 2021, we augment the model with the vaccination class to investigate the impact of vaccination rate and efficacy. We observe that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.

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“…These research works have a fundamental role in guiding public health authorities to better manage the pandemic. There were also studies 20 related to the analysis of conditions in which vaccines and other drugs can quickly lead to a community herd immunity to curtail the pandemic (Iboi et al, 2020;Gumel et al, 2021).…”

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confidence: 99%

COVID-19 and Scientific Research Interests and Findings in Epidemiology and Social Sciences: A Systematic Review

Be¹,

Alia²,

R³

2021

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The emergence of COVID-19 has prompted an unprecedented scientic publication with the aim of better understanding this new disease. This study assessed the scientic impact and disciplinary priorities of the published papers on the pandemic by comparing epidemiological (EP) and social sciences (SS) research interests. Papers were identified via keywords searching using Google Scholar and Scopus databases. From an initial 1720 papers, we identified 597 relevant articles, of which 347 were for EP researches and 250 for SS studies. We extracted information, such as authors' countries, and research thematic related to EP and SS. The results revealed that most papers were authored by Asian (37.5%), European (30.5%) and American (19.6%) scientists. Only 10.1% and 2.3% of authors were aliated with African and Oceanian institutions, respectively, indicating that the regions most affected by the pandemic mainly contributed to the scientic publications. In total, 26 research themes were recorded from both EP and SS studies. There was a high signicant dierence among themes in both research fields (Chi-square = 1204.3, df = 1, p-value < 0.001). EP papers mostly dealt with clinical trials (54.5%) and diagnosis (53.3%). These papers assessed the incidence and epidemiological characteristics of the disease (incubation period, symptomatic period, recovering or death), testing tests developed, drugs and vaccines used. SS papers were mainly concerned with the sociocultural analyses (78%) and economic impact (55.6%) of the pandemic. They mainly focused on behavioral changes induced by the pandemic and strategies developed to mitigate its impacts. This study highlights the difference between regions and gaps between scientific disciplines concerning the proposed responses to control the pandemic. It is important to promote collaborative and interdisciplinary studies for health emergencies.

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A primer on using mathematics to understand COVID-19 dynamics: Modeling, analysis and simulations

Cited by 133 publications

References 40 publications

Vaccination and herd immunity thresholds in heterogeneous populations

Vaccination and herd immunity thresholds in heterogeneous populations

Assessment of Vaccination and Underreporting on COVID-19 Infections in Turkey Based On Effective Reproduction Number

COVID-19 and Scientific Research Interests and Findings in Epidemiology and Social Sciences: A Systematic Review

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