Dynamics of a fractional-order rubella disease model with vertical transmission and saturated incidence rate

Embun Fivi Elivina, Wuryansari Muharini Kusumawinahyu, Marsudi -

Abstract


Rubella is one of the viruses responsible for rubella disease. If the rubella virus infects a pregnant woman during the first trimester of pregnancy, it causes CRS (the virus transmits vertically from mother to fetus). In this paper, we study the rubella disease model with a fractional-order derivative and saturated incidence rate. Infectious diseases have a history in their transmission dynamics, thus non-local operators such as fractional-order derivatives play a vital role in modeling the dynamics of such epidemics. First, we analyze the important mathematical features of the proposed model, such as the existence and uniqueness, the non-negativity and boundedness of solutions. Then, the equilibrium point, basic reproduction number, and stability of the equilibrium points are also investigated. The model has two equilibrium points, namely the disease-free equilibrium and endemic equilibrium. The disease-free equilibrium point always exists, while the endemic equilibrium point exists if R0>1. The disease-free equilibrium point is locally asymptotically stable if R0<1, while the endemic equilibrium point is locally asymptotically stable if the Routh-Hurwitz criterion is satisfied. Numerical simulation is done by using the Grunwald-Letnikov approximation method to confirm the results of analytical calculations.

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Published: 2023-12-29

How to Cite this Article:

Embun Fivi Elivina, Wuryansari Muharini Kusumawinahyu, Marsudi -, Dynamics of a fractional-order rubella disease model with vertical transmission and saturated incidence rate, Commun. Math. Biol. Neurosci., 2023 (2023), Article ID 137

Copyright © 2023 Embun Fivi Elivina, Wuryansari Muharini Kusumawinahyu, Marsudi -. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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