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This paper discusses the problem of social media addiction that pose a major threat to the human population especially children and teenagers. It is well known that Cognitive Behavioral Therapy (CBT) is an effective treatment to treat the addict individuals and delay in the treatment leads the patient to worst stage even to death. Therefore, it is important to identify the individuals who has addiction symptoms at early stage and to provide proper counseling. We propose and analyze a nonlinear mathematical model for social media addiction problem using case detection strategy to reduce the addiction. The basic reproduction number and equilibria of the model are computed. Further, the deterministic model is extended to delay differential equation model by incorporating transmission delay and treatment delay in the system. The local stability of different equilibria is discussed in detail. Additionally, the model is converted to stochastic model and numerical simulation is carried out to compare the results of both deterministic and stochastic model. Numerical result shows that the introduction of time delays can destabilize the model system and Hopf bifurcation occurs due to periodic oscillations when certain equilibrium point crosses the delay threshold limit. Our results of stochastic model show a smaller number of social media users and addict population when compared with deterministic model. Also, our results reveal that detection and counseling parameters play a vital role in reducing addiction population. Presented results clearly suggest that there is a need to use effective detection strategy and suitable counseling program to reduce the social media addiction level. [ABSTRACT FROM AUTHOR]

A five-dimensional delay differential system is proposed to describe oscillatory behaviour in microbial continuous culture. Stability and Hopf bifurcation are discussed, including the changing regularity of the bifurcation value. An explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and centre manifold. Finally, some numerical simulations are performed to illustrate the analytical results found. [ABSTRACT FROM AUTHOR]