Mathematical Modeling and its Stability Analysis of an SEIR Model to Control Dengue by Segregating the Infective: An Approach for Efficient Resource Allocation

Abstract

Objectives: Many research deals study on modeling the spread of dengue virus disease. The study dealing mathematical model to influence the concept of segregating infective is very important as it makes an organised practice of treatment which enlightens civilization. This article focuses on the same and frames a model with a proper analysis. Methods: BhirkoffRhota theorem helps in proving the boundedness of the model. By using the Next-Generation matrix the expression for Reproduction number is determined. The Routh-Hurwitz stability criterion is used to reveal the Local Stability of the proposed model. The aid of Lyapunov-LaSalle's principle proves the Global Stability. Findings: The proposed model is found to be positive and also bounded. Moreover, the equilibrium points exists and stable locally and globally. The numerical simulation shows that at the disease-free equilibrium and at the endemic equilibrium proving the stability of the model numerically. The comparative analysis of the model results in revealing the fact that the proposed model controls the infective better than the usual model. Novelty: The article differs from the usual model by incorporating the idea of categorizing the infected population into 3 phase namely febrile, critical and convalescent concluding that the use of proposed model helps in effective treatment and in efficient management of hospital resources in a systematic way. Keywords: Epidemic, Treatment Class, SEIR model, Jacobian matrix, Sensitivity index