In the investigations presented here, an efficient computing approach is applied to solve Human Immunodeficiency Virus (HIV) infection spread. This approach involves CD4+ T-cells by feed-forward artificial neural networks (FF-ANNs) trained with particle swarm optimization (PSO) and interior point method (IPM), i.e., FF-ANN-PSO-IPM. In the proposed solver FF-ANN-PSO-IPM, the FF-ANN models of differential equations are used to develop the fitness functions for an infection model of T-cells. The training of networks through minimization problem are proficiently conducted by integrated heuristic capability of PSO-IPM. The reliability, stability and exactness of the proposed FF-ANN-PSO-IPM are established through comparison with outcomes of standard numerical procedure with Adams method for both single and multiple autonomous trials with precision of order 4 to 8 decimal places of accuracy. The statistical measures are effectively used to validate the outcomes of the proposed FF-ANN-PSO-IPM.