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The Supplemental Nutrition Assistance Program (SNAP, also known as food stamps) offers tens of millions of American beneficiaries a crucial lifeline. This welfare benefit has been associated with better nutritional outcomes and has been linked to an efficient tool to fight hunger, improve labour market outcomes for the beneficiaries, achieve higher birth weight for children born to the beneficiary mothers, improve height and health outcomes for the beneficiaries. SNAP has been found to be an essential tool to ensure the availability of vital resources during times of need, etc. Despite the program's numerous advantages, serious doubts exist about its viability and stability of the program especially, given the steep rise in program costs over the years. Over the past 50 years, SNAP has experienced tremendous growth both in terms of the number of beneficiaries and amount of spending. From over $1.82 billion in 1969 to over $113 billion in 2022, the total cost of the SNAP initiative has increased over 62 times in 53 years. This research uses data from the US Department of Agriculture to investigate the time series properties in the rise in the total expenditure devoted to the SNAP between 1969 and 2022. With and without trends, Augmented Dickey-Fuller tests are run with carefully chosen lag lengths. The existence of a unit root cannot be rejected in all specifications pointing to the possibility that the program might have grown in an unstable manner over time. An overwhelming amount of evidence points to an unstable and unstable growth in the overall amount spent on SNAP recipients. This unchecked growth may present substantial difficulties for policymakers especially since the program competes with other welfare programs in an environment of rapidly rising national debt and persistent budget deficits. The report does not attempt to estimate program fraud or abuse which may partially contribute to higher expenditures.

This mathematical model is based on a system of two non-linear delay differential equations representing GDP (Gross Domestic Product) growth and national debt respectively. Growth of GDP is directly proportional to national debt. In the absence of national debt, there could be no or very slow GDP growth. The national debt is heavily dependent on external loans and external investments. These investments act as a catalyst for accelerating the rate of GDP. It is assumed that the external debt is never paid off fully. The availability of external investments is not immediate as per demand but takes some time for the maturation of the deal. The time delay in actual arrival of the foreign investment and its effect on GDP-National debt dynamics is the main focus of this study. This effect is studied using a delay parameter τ. The non-zero equilibrium of the system is calculated, and the stability analysis is performed on it. Hopf bifurcation is observed for a critical value of the delay parameter. Numerical simulation is performed using MATLAB code.

This mathematical model is based on a system of two non-linear delay differential equations representing GDP (Gross Domestic Product) growth and national debt respectively. Growth of GDP is directly proportional to national debt. In the absence of national debt, there could be no or very slow GDP growth. The national debt is heavily dependent on external loans and external investments. These investments act as a catalyst for accelerating the rate of GDP. It is assumed that the external debt is never paid off fully. The availability of external investments is not immediate as per demand but takes some time for the maturation of the deal. The time delay in actual arrival of the foreign investment and its effect on GDP-National debt dynamics is the main focus of this study. This effect is studied using a delay parameter τ. The non-zero equilibrium of the system is calculated, and the stability analysis is performed on it. Hopf bifurcation is observed for a critical value of the delay parameter. Numerical simulation is performed using MATLAB code. [ABSTRACT FROM AUTHOR]