# LOCAL AND GLOBAL STABILITY ANALYSIS OF MEASLES EPIDEMIC MODEL AT DISEASE-FREE EQUILIBRIUM

• Philip Onyema Ochi AMERICAN UNIVERSITY OF NIGERIA ACADEMY, YOLA
• Apeh Andrew Agada SKYLINE UNIVERSITY, NIGERIA
• Ifeoma B. Nworah 3Federal Institute of Industrial Research (FIIRO), North-East centre, Yola, Adamawa State
• Damascus Arinze Nworah Bioresources Development Centre, National Biotechnology Development Agency, Jalingo, Taraba State, Nigeria.
• Achi Nathan Goni Bethel Baptist High School, Kaduna, Nigeria
Keywords: Measles, SVEIR Model, Basic reproduction number, Local stability, Numerical simulation

### Abstract

In this study, a continuous mathematical model for the dynamics of Measles (rubeola) outbreak at constant recruitment rate was formulated. In the model, we partitioned the population into Susceptible (S), Vaccinated (V), exposed (E), Infected (I) and recovered (R) individuals. We analyzed a SVEIR compartmental nonlinear deterministic mathematical model of measles epidemic in a community with constant population. Analytical studies were carried out on the model using the method of linearized stability. The basic reproductive number R0 that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if R0<1  and unstable if R0 >1 respectively. Finally, we simulate the model system in MATLAB and obtained the graphical behavior of each compartment. From the simulation, we observed that the measles infection was eradicated in the environment when R0<1.

### Author Biographies

Philip Onyema Ochi, AMERICAN UNIVERSITY OF NIGERIA ACADEMY, YOLA

DEPARTMENT OF  MATHEMATICS AND MATHEMATICS TEACHER

Apeh Andrew Agada, SKYLINE UNIVERSITY, NIGERIA

MATHEMATICS DEPARTMENT AND LECTURER II

Ifeoma B. Nworah, 3Federal Institute of Industrial Research (FIIRO), North-East centre, Yola, Adamawa State

NIL

Achi Nathan Goni, Bethel Baptist High School, Kaduna, Nigeria

NIL

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Published
2024-03-19
How to Cite
OchiP. O., AgadaA. A., NworahI. B., NworahD. A., & GoniA. N. (2024). LOCAL AND GLOBAL STABILITY ANALYSIS OF MEASLES EPIDEMIC MODEL AT DISEASE-FREE EQUILIBRIUM. FUDMA JOURNAL OF SCIENCES, 8(1), 369 - 379. https://doi.org/10.33003/fjs-2024-0801-2219
Section
Research Articles