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

• Published in: International journal of applied and computational mathematics Vol. 4; no. 5; p. 118
• Main Authors: Mathur, Kunwer Singh, Narayan, Prakash
• Format: Journal Article
• Language: English
• 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
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-018-0548-0

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.