Helicobacter pylori colonizes half of the world's population as the dominant member of the gastric microbiota resulting in a lifelong chronic infection. Host responses toward the bacterium can result in asymptomatic, pathogenic or even favorable health outcomes; however, mechanisms underlying the dual role of H. pylori as a commensal versus pathogenic organism are not well characterized. Recent evidence suggests mononuclear phagocytes are largely involved in shaping dominant immunity during infection mediating the balance between host tolerance and succumbing to overt disease. We combined computational modeling, bioinformatics and experimental validation in order to investigate interactions between macrophages and intracellular H. pylori. Global transcriptomic analysis on bone marrow-derived macrophages (BMDM) in a gentamycin protection assay at six time points unveiled the presence of three sequential host response waves: an early transient regulatory gene module followed by sustained and late effector responses. Kinetic behaviors of pattern recognition receptors (PRRs) are linked to differential expression of spatiotemporal response waves and function to induce effector immunity through extracellular and intracellular detection of H. pylori. We report that bacterial interaction with the host intracellular environment caused significant suppression of regulatory NLRC3 and NLRX1 in a pattern inverse to early regulatory responses. To further delineate complex immune responses and pathway crosstalk between effector and regulatory PRRs, we built a computational model calibrated using time-series RNAseq data. Our validated computational hypotheses are that: 1) NLRX1 expression regulates bacterial burden in macrophages; and 2) early host response cytokines down-regulate NLRX1 expression through a negative feedback circuit. This paper applies modeling approaches to characterize the regulatory role of NLRX1 in mechanisms of host tolerance employed by macrophages to respond to and/or to co-exist with intracellular H. pylori.