Abstract
The applications of graph theory in the area of networking are of great significance in system analysis of different varieties, including biological systems. In biological systems, the use of networks finds importance in the study of epidemic and its control. A practical example include the evaluation of the spread of disease within human population and the impact of awareness circulating admist the same population as a result of the infection. Agaba et al. in 2017 proposed a mathematical model that analysed the impact of awareness on the spread of infectious diseases. This was done using the stability analyses of the various steady states of the system of equations and also through the evaluation of some numerical simulations. This paper, with the aid of the system of equations developed by Agaba et al., 2017b, studies the impact of awareness spreading simultaneously with an infectious disease within human population using weighted network.
Highlights
Researches on the creation and dissemination of human awareness regarding the spread of an epidemic have been carried out by many scholars in diverse dimensions
While other research works that analysed the impact of awareness creation and dissemination on the spread of infectious diseases considered networkbased models
The results from the aforementioned analyses revealed the importance of human awareness in controlling, and in some cases eradicating, infectious diseases from the entire population as portrait by (Agaba et al, 2017b; Agaba et al, 2017c; Ferguson, 2007; Funk et al, 2010; Jones and Salathé, 2009; Nishiura et al, 2005; Pruyt et al, 2015)
Summary
Researches on the creation and dissemination of human awareness regarding the spread of an epidemic have been carried out by many scholars in diverse dimensions. Rosen (2012) and Newman (2004) considered some illustrations of graph models involving individuals and groups of individuals Among these examples is a transportation network wherein airline networks were modelled by representing each airport by a vertex (node) and all flights by a particular airline moving each day from an airport (departure) to another airport (destination) by directed edges. This paper considered a network in which the nodes represent groups of individuals determined by their disease and awareness status, while the edges denote the connections between the nodes as a result of the transition of individuals from one node to the other with directed edges indicating the direction of their transitions. If the entire human population within the network is denoted by , the proportion of each individual on the disease and awareness network is given respectively as: and
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
