Analysis of mathematical model for the impact of word of mouth and social media in marketing

El-Sayed, Ghada M.; Arafa, Ayman A.; Soliman, Ahmed A.; Mahmoud, Gamal M.

doi:10.21608/sjsci.2025.345701.1244

Analysis of mathematical model for the impact of word of mouth and social media in marketing

Document Type : Regular Articles

Authors

¹ Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.

² Institute of Basic and Applied Sciences, Egypt-Japan University of Science and Technology, Alexandria, Egypt.

³ Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt.

10.21608/sjsci.2025.345701.1244

Abstract

Social media advertising is creating a revolution in digital marketing. It offers businesses an unparalleled and significant opportunity to instantly connect with millions of active users around the world. This paper presents a marketing model that merges two pivotal approaches: direct word-of-mouth promotion and advertisements on social media platforms. The model is used to examine their critical impact on consumer behavior. The existence of steady states is explored through graphical representations of nullclines, and their local stability is examined using the coefficients of the characteristic equation. Our research suggests that the model undergoes a Hopf bifurcation, which highlights the presence of periodic solutions. Additionally, a sensitivity analysis is performed to evaluate how changes in parameters impact clients. Our main findings emphasize the substantial impact of social media advertising on sales. Consequently, the model offers valuable and perceptible insights for developing effective promotional strategies. These strategies drive consumer engagement and increase revenue.

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