A Mathematical Model on Cholera Outbreak with Vaccination

Bolanle Adeola Olokuntoye

Bolanle Adeola Olokuntoye Obafemi Awolowo University, Ile-Ife, Nigeria

Keywords: Cholera, SIRB model, Vaccination, Equilibrium points, Reproduction number, Epidemiological modeling

Abstract

This study develops and analyzes a cholera transmission model of SIRB type (Sus-
ceptible–Infected–Recovered–Bacteria) that incorporates vaccination. The main
objective is to investigate the threshold conditions under which cholera can either
be eradicated or persist in the community. The model formulation captures both
direct person-to-person transmission and indirect infection through contaminated
water. Using standard dynamical systems techniques, the disease-free equilibrium
(DFE) and endemic equilibrium (EE) were derived. The next-generation matrix
approach was then applied to obtain the basic reproduction number, R0, which
serves as the central threshold parameter governing disease dynamics. The analysis
showed that the DFE is locally asymptotically stable whenever R0 < 1, implying
cholera elimination under effective interventions, while the EE exists and is locally
stable when R0 > 1, confirming sustained disease persistence. These results em-
phasize the importance of vaccination and improvements in sanitation as essential
strategies to reduce R0 below unity and achieve long-term cholera control

Author Biography

Bolanle Adeola Olokuntoye, Obafemi Awolowo University, Ile-Ife, Nigeria

Department of Mathematics,

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