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The limited availability of formal jobs in developing nations always heightens the challenge for unemployed individuals in securing regular employment. Temporary employment in the informal sector serves as a source to fulfill their basic needs and enhance their employable skills. In this paper, we introduce a nonlinear mathematical model to study the effect of informal and formal jobs on the dynamics of unemployment. For the model formulation, we categorize the labor force into three classes: unemployed, temporary employed, and regularly employed. A separate dynamical variable is used to represent the available temporary vacancies. It is assumed that temporarily employed individuals may transition into regular employment or self-employment. Furthermore, self-employed individuals contribute to generating temporary vacancies within the informal sector. The long-term behavior of the proposed system is analyzed using the qualitative theory of differential equations. A quantity known as the reproduction number of the system is derived, and it is found that the occurrence of multiple bifurcations for the proposed system is influenced by the value of this threshold quantity. Furthermore, we validate our analytical findings numerically. The findings of this study illustrate that an increase in the shifting rate of individuals from temporary to regular employment is not always effective in increasing the number of regularly employed individuals. Additionally, an increase in the transition of temporarily employed individuals into self-employment, coupled with their involvement in creating more temporary jobs, proves beneficial in reducing unemployment. [ABSTRACT FROM AUTHOR]

Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility of equilibria and their stability properties are discussed. A pertinent quantity ( ℛ 0 ), known as the reproduction number, is calculated and it is shown that the formulated system undergoes transcritical, saddle-node, Hopf and Bogdanov–Takens bifurcations on the variation of ℛ 0 . The analytically obtained results are validated through numerical simulations. The results obtained from this study indicate that a substantial rate of job generation by self-employed individuals has a stabilizing effect on the system. Moreover, self-employment along with informal skill acquisition through engaging in informal work proves to be an effective measure in curbing the issue of unemployment in society. [ABSTRACT FROM AUTHOR]

Diabetes is a widespread non-contagious disease, and a significant fraction of human population in the world is affected by it. Lifestyle changes including physical activities and a healthy diet can prevent or delay the onset of diabetes and its complications. In this paper, nonlinear mathematical models are proposed and analyzed to study the role of awareness in the prevention of diabetes. In model formulation, first it is assumed that the unaware people become aware through word-of-mouth communication only and adopt a preventive lifestyle to reduce the peril of diabetes. Subsequently, the proposed model is extended by incorporating the effect of social media and TV advertisements on diabetes awareness. An awareness generation number is obtained for the first model and it is found that the system exhibits transcritical bifurcation when this number crosses unity. Both models are analyzed qualitatively and a comparison of outcomes reveals that social media and TV ads are more effective in raising the level of awareness among individuals and helps to inhibit the risk of diabetes mellitus. The analytical results are verified through numerical simulation. [ABSTRACT FROM AUTHOR]