Dynamical transmission of Varicella Virus in Jordan with SVIR Model  through analysis and numerical simulations

Manal Ghannam

doi:10.48165/jmmfc.2024

Authors

Manal Ghannam Faculty of Art and Sciences, Department of Mathematics, Near East University, Northren Cyprus, Turkey

DOI:

https://doi.org/10.48165/jmmfc.2024

Keywords:

Varicella virus, Routh-Hurwitz stability, Sensitivity analysis, Basic reproduction Number.

Abstract

Chickenpox, another name for varicella virus, is a highly contagious illness. In this work, we use mathematical modelling and simulation to examine the dynamics of transmission and propose an SVIR model for the varicella virus in Jordan. The dynamics of the population in various classes are examined using a suggested model, which offers a more thorough comprehension of the course of the epidemic and the efficacy of control efforts. Lipschitz condition and fixed-point theory were also used to establish the solution's existence and uniqueness. Additionally, using figures and mathematics, it investigates the effects of different factors on the reproductive number and sensitivity analysis of the suggested model. The Routh-Hurwitz stability criterion is used to determine local stability at equilibrium sites that are both disease-free and endemic. Lyapunov functions with the first derivative test used to establish the global stability of model equilibria analysis for both >1 and <1. the suggested model is numerically simulated using Matlab software to ascertain how parameters affect the scenarios. The findings of this study confirm the theoretical and biological phenomena of the model and aid in elucidating the mechanisms of varicella virus transmission and directing public safety policy decisions. In the conclusion, Since the varicella virus puts a lot of demand on the country's healthcare system, the Jordanian Ministry of Health should launch vaccination campaigns in order to eliminate the disease because a universal varicella vaccination is necessary. Long-lasting protection from varicella immunization lowers the risk of epidemics and promotes community health, and lowering the overall burden of varicella virus infection frees up funds for other health concerns.

Author Biography

Manal Ghannam, Faculty of Art and Sciences, Department of Mathematics, Near East University, Northren Cyprus, Turkey

Mathematical research center, Near East University, Northren Cyprus, Turkey

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