MATHEMATICAL MODELING ON TRANSMISSION DYNAMICS OF PNEUMONIA INFECTION WITH INTERVENTION INCORPORATING INTERNATIONAL TRAVELLERS SCREENING
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Date
2024-08
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THE CATHOLIC UNIVERSITY OF EASTERN AFRICA
Abstract
Pneumonia is one of the global pandemics which have afflicted humanity in various aspects of life among the young children and elderly one. In some developed countries like Kenya, it is discovered to be a highly airborne transmitted disease which leads to a high mortality rate of human beings. It has been discovered by the World Health Organization (WHO) that almost 16% deaths of children are due to pneumonia infection in most regions like South Asia and
Sub-Sahara Africa. There exist several mathematical models which aimed at mitigating the transmission of Pneumonia infection. We take into consideration the screening of international travellers with intervention seeking to minimize the rate of the circulation of pneumonia infection led by the movement of human beings. The originality of this research lies on International Travellers Screening as a preventive and control mechanism of pneumonia transmission. We
create and examine the pneumonia disease dynamics from a mathematical view using SXEIT model. The model includes five non-linear compartments namely; "Susceptible (S), Screened (X), Exposed (E), Infected (I) and Treated (T)". Also, we develop the Basic Reproduction number (Ro) in the study and examine the existence of all the equilibrium points; the Endemic equilibrium and Disease Free equilibrium, and analyze their stabilities. If the basic reproduction
number R0 > 1, it records that the endemic equilibrium is globally stable and the disease persists, while if R0 < 1, then the disease will be eradicated out of the population. The model uses the preferred model system of differential equations which is subjected to numerical simulation using Matlab application. The research utilizes data collected from surveys of other writers and related works to parameterize and validate the model. The findings of this study are
recommended to the Ministry of Health and World Health Organization (WHO) who may use them to strategize new ways of preventing the spread of Pneumonia infection.
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Keywords
Compartmental models, Susceptible-Infected-Recovered (SIR) models, disease control strategies, intervention strategies, infection dynamics