Free-roaming dogs can present significant challenges to public health, wildlife conservation, and livestock production. Their own welfare may also be a concern, as free-roaming dogs can experience poor health and welfare. Dog population management is widely conducted to mitigate these issues. To ensure efficient use of resources, it is critical that effective, cost-efficient, and high-welfare strategies are identified. The dog population comprises distinct subpopulations characterised by their restriction status and level of ownership, but the assessment of dog population management often fails to consider the impact of the interaction between subpopulations on management success. We present a system dynamics model that incorporates an interactive and dynamic system of dog subpopulations. We identify that methods incorporating both fertility control and responsible ownership interventions (a reduction in abandonment and an increase in shelter adoptions) have the greatest potential to reduce free-roaming dog population sizes over longer periods of time, whilst being cost-effective and improving overall welfare. We suggest that future management should be applied at high levels of coverage and should target all sources of population increase, such as abandonment, births, and free-roaming owned dogs, to ensure effective and cost-efficient reduction in free-roaming dog numbers.