Incidence and risk factors of malaria with hematological and immunological evaluation and integrable analysis of a fractional mathematical model

Malaria during pregnancy remains a major public health challenge, contributing to maternal anemia, low birth weight, stillbirth, and preterm delivery. This study investigated the prevalence of malaria among 400 pregnant women and evaluated its associated risk factors, hematological alterations, and inflammatory responses, including tumor necrosis factor-alpha (TNF-$$\alpha$$) and interferon-gamma (IFN-$$\gamma$$). Anti-Plasmodium IgM and IgG antibodies, TNF-$$\alpha$$, and IFN-$$\gamma$$ were measured using ELISA, while hematological indices were assessed using a Coulter counter. The overall malaria prevalence was 51.2%, with 68.3% IgG and 31.7% IgM seropositivity among infected cases. Infection was significantly associated with age, residence, education level, animal husbandry, and housing conditions. Infected women exhibited significant reductions in red blood cell count, hemoglobin, and hematocrit, alongside elevated white blood cell counts and pro-inflammatory cytokines (TNF-$$\alpha$$ and IFN-$$\gamma$$). Motivated by these clinical findings, we further analyzed an established mathematical model of malaria in pregnancy within the $${\text{\L } }^\mathfrak {p}$$ framework. We proved the existence of a $$\mathfrak {p}$$-integrable solution using the Leray–Schauder nonlinear alternative and the Banach fixed-point theorem, and examined stability in the sense of Ulam–Hyers and Ulam–Hyers–Rassias. Numerical simulations generated using MATLAB illustrate and support the theoretical results. To the best of our knowledge, this study contributes to the analytical investigation of malaria-in-pregnancy models within the $${\text{\L } }^\mathfrak {p}$$ setting, highlighting its mathematical significance.