Dynamics of an SVEIRS Epidemic Model with Vaccination and Saturated Incidence Rate

Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immun...

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Published inInternational journal of applied and computational mathematics Vol. 4; no. 5; p. 118
Main Authors Mathur, Kunwer Singh, Narayan, Prakash
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 2018
Springer Nature B.V
Subjects
Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Epidemics
Immunity
Incidence
Influenza
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Measles
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Theoretical
Saturated incidence rate
Global stability
Reproduction number
Pre and post vaccinations
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Abstract Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number R v , which is determined by the next-generation approach and obtained that if R v ≤ 1 , the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for R v > 1 , a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.
AbstractList Measles and influenza are two major diseases-caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number R v , which is determined by the next-generation approach and obtained that if R v ≤ 1 , the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for R v > 1 , a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.
Measles and influenza are two major diseases-caused an epidemic in India. Therefore, in this paper, a epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number , which is determined by the next-generation approach and obtained that if , the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for , a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.
Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number Rv, which is determined by the next-generation approach and obtained that if Rv≤1, the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for Rv>1, a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.
Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and influenza is proposed and analyzed, where pre and post vaccinations are considered as control strategies with waning natural, vaccine-induced immunity and saturation incidence rate. The dissection of the proposed model is conferred in terms of the associated reproduction number R v , which is determined by the next-generation approach and obtained that if R v ≤ 1 , the disease-free equilibrium exists and it is locally as well as globally asymptotically stable. Further for R v > 1 , a unique endemic equilibrium exists and it is also locally as well as globally asymptotically stable under certain conditions, which shows the prevalence and persistence of the disease in the population.
ArticleNumber 118
Author Mathur, Kunwer Singh
Narayan, Prakash
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Issue 5
Keywords Saturated incidence rate
Global stability
Reproduction number
Pre and post vaccinations
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Snippet Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and...
Measles and influenza are two major diseases-caused an epidemic in India. Therefore, in this paper, a epidemic mathematical model for measles and influenza is...
Measles and influenza are two major diseases–caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and...
Measles and influenza are two major diseases-caused an epidemic in India. Therefore, in this paper, a SVEIRS epidemic mathematical model for measles and...
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SubjectTerms Applications of Mathematics
Applied mathematics
Computational mathematics
Computational Science and Engineering
Epidemics
Immunity
Incidence
Influenza
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Measles
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Theoretical
Title Dynamics of an SVEIRS Epidemic Model with Vaccination and Saturated Incidence Rate
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https://www.ncbi.nlm.nih.gov/pubmed/32289048
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