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Stevelab, LLC is working on an app that will be released within the year. For planning purposes, the company needs to be able to predict how well the app will spread in its initial phase. Because the pilot launch will be limited to Hillsborough County, FL, there is a limited population. The marketing strategy is to sell the application to places where people gather to mingle and socialize, with a particular focus to the bar scene. Customers of the bar can use the app for free. In addition to our direct sales efforts, we can expect the bar owners to talk to other owners, users will talk to other people, and users will talk to other bar employees creating a web of additional growth. These components are very similar to an SIR model used to predict the spread of infection by dividing a population into 3 categories, Susceptible, Infected, and Recovered. Ratios are applied to show how each division interacts with the other two. (Nicho, 2010) Adding a vector as a means of transmission gives a second population to track divided into 3 similar categories. (Wei, Li, & Martcheva, 2007) In addition to reactions among these three, there are also constants to represent how the two populations interact. This study tests the viability of using an SIR vector model to predict sales of our new app. We conclude that there are good matches between the biological data points and the business data points making the use of an SIR model for this purpose plausible and a prediction can be made. Due to pervasive estimations in actual figures, the predictions are not expected to be extremely accurate at this time. However, we have the ability to directly monitor all of these points as they happen, meaning we can use the same model with increasing accuracy as business progresses, even as early as our first week.

undergraduate journal of mathematical modeling

Using the SIR Epidemiology Model with Vector Transmission to Predict the Effectiveness of a Viral Marketing Campaign and the Spread of Product Adoption