Basic reproduction number and sensitivity analysis of Legionnaires’ disease model

Hamza Garba Ahmad; Felix Yakubu Eguda; Bulama Mohammed Lawan; James Andrawus; Babangida Ibrahim Babura

doi:10.54117/gjpas.v2i1.60

Authors

Hamza Garba Ahmad Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria.
Felix Yakubu Eguda Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria.
Bulama Mohammed Lawan Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria.
James Andrawus Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria.
Babangida Ibrahim Babura Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria.

DOI:

https://doi.org/10.54117/gjpas.v2i1.60

Keywords:

Legionnaires’ model, Reproduction number, Sensitivity analysis, Pneumonia, Disease

Abstract

Legionnaires’ disease is a very serious type of pneumonia (lung infection) caused by bacteria called Legionella. In this research, a mathematical model for the transmission dynamics of legionnaires’ is developed. Four different reproduction numbers were obtained indicating the type of interaction between susceptible and infected and how the disease is propagated between adults and children and vice versa. The research shows that using the human control reproduction number as response function, the sensitive parameters in the formulated system are the transmission probability, pubic enlighten awareness, modification parameter, progression rate, recover rate and natural mortality rate.

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