Background: Since 2017, the Palembang City Agriculture and Food Security Office has implemented a Pegagan duck livestock assistance program to alleviate poverty in Gandus District. However, its impact on poverty alleviation has never been formally evaluated. This study is urgently needed to assess the program’s effectiveness, provide evidence for improving its implementation, and support its potential replication in other districts of Palembang City. Objective: This study aims to (i) develop a poverty alleviation model for livestock business households, (ii) evaluate the distribution of poverty alleviation program assistance by the Palembang City Agriculture and Food Security Office, and (iii) map poor families in Gandus District using Geographic Information System (GIS) software. Methods: Data were collected through library research and field research. Two analytical techniques were employed: Structural Equation Modeling–Partial Least Squares (SEM-PLS) analysis and mapping of poor families using a Geographic Information System (GIS). Results: The SEM-PLS analysis revealed that investment had a positive and significant effect on welfare (t-statistic = 3.744, p = 0.000), while poverty had a significant effect on income (t-statistic = 2.978, p = 0.003). However, the relationships between income and investment, income and consumption, and poverty and welfare were not statistically significant. Poverty mapping using GIS showed that Pulokerto Village had the highest poverty rate (10.25%), whereas Karang Jaya Village had the lowest (6.54%) among the five villages in Gandus District. Conclusion: Investment significantly improves household welfare, while poverty significantly affects household income. GIS mapping also revealed spatial differences in poverty levels among villages in Gandus District, supporting more targeted poverty alleviation efforts.