Mathematical Propagation for the Treatment and Vaccination of a Generalized Well-Posed SEIR Infectious Model

Bassey Echeng Bassey; Igwe O. Ewona; Adagba Odey Henry

doi:10.59828/pijms.v1i2.12

Authors

Bassey Echeng Bassey Department of Mathematics, University of Cross River State – (Unicross), Calabar, Nigeria Author https://orcid.org/0000-0001-7070-8176
Igwe O. Ewona Department of Physics, University of Cross River State – (Unicross), Calabar, Nigeria Author
Adagba Odey Henry Department of Industrial mathematics and Applied Statistics Ebonyi State University, Abakaliki, Nigeria Author

DOI:

https://doi.org/10.59828/pijms.v1i2.12

Keywords:

Generalized-SEIR-model, system-well-posedness, bilinear-control-functions, Lipschitz-condition, existence-uniqueness, state-space.

Abstract

In this paper, we proposed a generalized theoretical executable investigation for an improved SEIR mathematical model for infectious diseases. The model was constructed to determine a solution for a system of ordinary differential equations described in a deterministic immune population and studied under designated bilinear control functions. Analytic predictions for the system's well-posedness were quantitatively conducted using the theory of ordinary differential equations in conjunction with the Lipschitz condition. An expression is obtained for the state-space, and numerical computations are determined. Results show that with induced bilinear control functions, rapid rejuvenation of the recovered and the susceptible was tremendously achieved. Moreso, the model exhibited compatibility for varying infectious diseases, provided there exists coherence to designated control functions. Therefore, the application of an improved generalized SEIR model under bilinear control functions is priori innovative for the amelioration and treatment of infectious diseases when compared with the results of existing SIR models.