Determination of the presence in the blood of antibodies specific to the causative agent of a particular disease (serodiagnosis) is an effective approach in medical analytical chemistry. Serodiagnostics performed in the lateral flow immunoassay format (immunochromatography) meet the modern requirements for point-of-care testing and are supported by existing technologies of large-scale diagnostic tests production—thus raising increased attention in a tense epidemiological situation. For traditional lateral flow serodiagnostics formats, a large number of nonspecific immunoglobulins in the sample significantly reduces the degree of detectable binding. To overcome these limitations, an assay based on the formation of immobilized antigen— specific antibody—labeled antigen complexes detection was proposed. However, the requirements for its implementation, providing maximum sensitivity, have not been established. This article describes the mathematical model for the above assay. The influence of the ratio of reagent concentrations on the analysis results is considered. It is noted that the formation of specific antibody complexes with several labeled antigens is the main limiting factor in reducing the detection limit, and methods are proposed to minimize this factor. Recommendations for the choice of the assay conditions, following from the analysis of the model, are confirmed experimentally.