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Qualitative Analysis of a Mathematical Model in the Time of COVID-19.

ABSTRACT: In this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam's type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.

SUBMITTER: Shah K

PROVIDER: S-EPMC7273369 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Qualitative Analysis of a Mathematical Model in the Time of COVID-19.

Shah Kamal K Abdeljawad Thabet T Mahariq Ibrahim I Jarad Fahd F

BioMed research international 20200525

In this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, ...[more]

PMID: 32596319

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Project description:ObjectivesTo investigate the impact of targeted vaccination strategies on morbidity and mortality due to COVID-19, as well as on the incidence of SARS-CoV-2, in India.DesignMathematical modelling.SettingsIndian epidemic of COVID-19 and vulnerable population.Data sourcesCountry-specific and age-segregated pattern of social contact, case fatality rate and demographic data obtained from peer-reviewed literature and public domain.ModelAn age-structured dynamical model describing SARS-CoV-2 transmission in India incorporating uncertainty in natural history parameters was constructed.InterventionsComparison of different vaccine strategies by targeting priority groups such as keyworkers including healthcare professionals, individuals with comorbidities (24-60 years old) and all above 60.Main outcome measuresIncidence reduction and averted deaths in different scenarios, assuming that the current restrictions are fully lifted as vaccination is implemented.ResultsThe priority groups together account for about 18% of India's population. An infection-preventing vaccine with 60% efficacy covering all these groups would reduce peak symptomatic incidence by 20.6% (95% uncertainty intervals (UI) 16.7-25.4) and cumulative mortality by 29.7% (95% CrI 25.8-33.8). A similar vaccine with ability to prevent symptoms (but not infection) will reduce peak incidence of symptomatic cases by 10.4% (95% CrI 8.4-13.0) and cumulative mortality by 32.9% (95% CrI 28.6-37.3). In the event of insufficient vaccine supply to cover all priority groups, model projections suggest that after keyworkers, vaccine strategy should prioritise all who are >60 and subsequently individuals with comorbidities. In settings with weakest transmission, such as sparsely populated rural areas, those with comorbidities should be prioritised after keyworkers.ConclusionsAn appropriately targeted vaccination strategy would witness substantial mitigation of impact of COVID-19 in a country like India with wide heterogeneity. 'Smart vaccination', based on public health considerations, rather than mass vaccination, appears prudent.

Dataset Information

Qualitative Analysis of a Mathematical Model in the Time of COVID-19.

Publications

Qualitative Analysis of a Mathematical Model in the Time of COVID-19.

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