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We develop a methodology for modeling post-earthquake hospital needs and accessibility, coupling a probabilistic regional casualty risk model with a novel agent-based human behavior model. We use it to study hospital transportation in two socio-economically distinct districts of Lima, Peru, after a hypothetical moment magnitude 8.0 event. Our work provides insights into the infrastructure and socio-economic vulnerability factors that determine timely healthcare access, across various hypothetical behavioral and policy contexts/scenarios. In the baseline scenario that assumes households respond to the emergency independently (i.e. transport only their own members to hospital) but there is coordination among hospitals (i.e. ambulance sharing), car ownership is key for rapid healthcare access. Twenty-four percent of non-life-threatening casualties in the district with 57% car ownership will arrive at hospital in the first 45 min; only 6% of such patients in the more economically deprived district (18% car ownership) will reach hospital in that time. If car-owning neighbors help transporting patients without cars, over 96% of non-life-threatening casualties will reach hospital in the first 45 min in both districts, significantly reducing intra-regional disparities in healthcare access. Arrival times would nearly halve compared to the baseline scenario if the number of available ambulances doubled. If hospitals do not share ambulances, arrival times of non-life-threatening and threatening casualties show a notable reduction in one district (by 56% and 42%, respectively) but a significant increase in the other, more economically deprived district (by 109% and 97%, respectively), compared to the baseline case. The arrival times presented in this study are specific to the studied context, and the appropriate assumptions made. We benchmark the performance of the methodology using patient arrival times from the 2023 Turkey-Syria earthquake, yielding an acceptable outcome (i.e. similar temporal trends in the proportion of hospital arrivals). The findings can be leveraged for planning effective post-earthquake emergency response strategies.