Modelling the prevalence of prostitution under the influence of poverty: A deterministic vs. stochastic approach

Globally, there is a widespread awareness of poverty-related challenges. It's important to acknowledge that poverty is one of the key factors influencing prostitution. Addressing the rise in prostitution due to economic challenges is a major concern among the general public. In that scenario, many poor family girls/women were ready to downgrade their status for their family welfare and necessary needs. On that aspect, they are indulging in prostitution also because of their inability to do any other work. Particularly in the pandemic and lockdown, the situation is worsening for such people. To overcome these challenges, multi-angled and effective approaches have been adopted. We have formulated a nonlinear mathematical model to investigate the dynamics around prostitution due to impoverishment. Our model exhibits two equilibrium points, which are analyzed through a stability analysis. The threshold $R_0$ has determined and investigated its significant parameters for the spread of prostitution through numerical simulation. Further, we extended this model to a stochastic model to know its real nature. We have examined and contrasted the deterministic and stochastic outcomes pertaining to the behavior of significant parameters within this model. Our findings show better results in both the deterministic and stochastic natures. Moreover, we calibrated our model using data on sex workers. Our projections, derived from this fitting process, suggest a subsequent decline in the sex-worker population after 2023.