Emergency response preparedness increases disaster resilience and mitigates its possible impacts, mostly in public health emergencies. Prompt activation of these response plans and rapid optimization of delivery models and are essential for effective management of emergencies and disaster. In this paper, existing computational models and algorithms for routing deliveries and logistics during public health emergencies are identified. An overview of recent developments of optimization models and contributions, with emphasis on their applications in situations of uncertainties and unreliability, as obtainable in low-resource countries, is presented. Specific recent improvements in biologically-inspired and intelligent algorithms, genetic algorithms, and artificial immune systems techniques are surveyed. The research gaps are identified, and suggestions for potential future research concentrations are proffered.