Journal of Advances in Mathematics and Computer Science

The ability of the immune system to detect and eliminate most pathogens is essential for the survival of lower respiratory tract infection in 2016 by Olubadeji [1]. Lower respiratory tract infection (LRTI) constituted the second leading cause of death in all age bracket in Nigeria, Loddenkemper [2] said that Chronic lower respiratory diseases rank as the third leading cause of death in the United States. Intense research has been on how to reduce the spread of infection, which involves the mathematical modelling of the spread of infection based on mathematical epidemiological approach, This is necessary because a threshold cannot be discerned from the data generated from the Hospitals, rather it requires a mathematical model to analyze and simulate the LRTI dynamics on the enviroment. It also enables the calculation of the basic reproductive number (R₀) which is an important threshold for determining whether the environments are at risk or not.  In this paper, we adopt the susceptible- Exposed-infected-recovered-susceptible (SEIRS) model to depict the spread of infections in our environment. We qualitatively   analyze the model and establish that the virus-free state is locally asymptotically stable provided the basic reproduction number is less than unity. We solved the model numerically and simulate the solution for different scenarios on the network. The findings from our simulations are discussed.