The current work provides a mathematical second order perturbed singular delay differential model 

(SOPSDDM) by using the standard form of the LaneEmden model. The inclusive structures based 

on the delay terms, singularpoint and perturbation factor and shape forms of the SOPSDDM are 

provided. The novel form of the SOPSDDM is numerically solved by using the procedures of artificial 

neural networks (ANNs) along with the optimization measures based on the swarming procedures 

(PSO) and interiorpoint algorithm (IPA). An error function is optimized through the swarming PSO 

procedure along with the IPA to solve the SOPSDDM. The precision, substantiation and validation are 

observed for three problems of the SOPSDDM. The exactness of the novel SOPSDDM is observed by 

comparing the obtained and exact solutions. The reliability, stability and convergence of the proposed 

stochastic algorithms are observed for 30 independent trials to solve the novel SOPSDDM.