MATHEMATICAL MODELLING WITH OPTIMAL CONTROL OF INFECTIOUS DISEASES WITH VACCINATION

Articles in Press

Document Type : Research Paper

Authors

1 Chuka University, Chuka, Kenya.

2 Mama Ngina University College, Gatundu, Kenya.

Abstract

Mathematical models are critical in provision of information to the development of infections. Notwithstanding the effectiveness of vaccines, some vaccinated individuals nonetheless get infected. To deal with this, non- pharmaceutical measures inclusive of social distancing and handwashing are encouraged. This study offers a mathematical version that combines the effects of vaccination and social distancing, utilizing Kermack-McKendrick compartments and ordinary Differential Equations (ODEs). The study determines the basic reproduction number (R_0) by the use of the Next Generation Matrix (NGM). If R_0 is less than 1, the ailment will in the end die out; if R_0 is more than 1, the ailment
will continue to spread. Python simulations show that while vaccination and social distancing can
reduce transmission, they may be not sufficient to eliminate the disease entirely. Isolation is critical for reducing transmission similarly. The efficacy of vaccines and the vaccination rate are crucial additives of vaccination strategy. These techniques provide extra time for public health officers to put in force further measures, supplementing current processes. As we continue to come upon new and evolving health challenges, the mixing of most reliable management strategies into epidemic modelling may be important. Further studies and interdisciplinary collaboration will enhance our capability to combat infectious sicknesses and guard worldwide fitness.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 10 March 2025

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History

  • Receive Date: 04 July 2024
  • Revise Date: 29 November 2024
  • Accept Date: 03 March 2025

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