Analyzing the Dynamics of a Periodic Typhoid Fever Transmission Model with Imperfect Vaccination

Mohammed H. Alharbi, Fawaz K. Alalhareth and Mahmoud A. Ibrahim ()
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Mohammed H. Alharbi: Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
Fawaz K. Alalhareth: Department of Mathematics, College of Arts & Sciences, Najran University, Najran 61441, Saudi Arabia
Mahmoud A. Ibrahim: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

Mathematics, 2023, vol. 11, issue 15, 1-26

Abstract: We present a nonautonomous compartmental model that incorporates vaccination and accounts for the seasonal transmission of typhoid fever. The dynamics of the system are governed by the basic reproductive number R 0 . This demonstrates the global stability of the disease-free solution if R 0 < 1 . On the contrary, if R 0 > 1 , the disease persists and positive periodic solutions exist. Numerical simulations validate our theoretical findings. To accurately fit typhoid fever data in Taiwan from 2008 to 2023, we use the model and estimate its parameters using Latin hypercube sampling and least squares techniques. A sensitivity analysis reveals the significant influence of parameters such as infection rates on the reproduction number. Increasing vaccination coverage, despite challenges in developing countries, reduces typhoid cases. Accessible and highly effective vaccines play a critical role in suppressing the epidemic, outweighing concerns about the efficacy of the vaccine. Investigating possible parameter changes in Taiwan highlights the importance of monitoring and managing transmission rates to prevent recurring annual epidemics.

Keywords: typhoid fever; seasonal model; partially susceptible; reproduction numbers; global stability; periodic solutions; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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