Fractional Caputo and sensitivity heat map for a gonorrhea transmission model in a sex structured population

Abstract

Gonorrhea is a disease that is spread by sexual contact, and it can potentially cause infections in the genital region, the rectum, and even the throat. Due to the shared history between infected individuals and their sexual partners, infected individuals will likely continue to have sexual relations with those same partners. As a result, this article aims to investigate how memory affects the transmission of gonorrhea in a structured population using the Caputo fractional derivative and sensitivity analysis. The model is shown to be positively invariant with a unique bound. The existence and uniqueness criteria of the fractional model are established using fixed-point theory. The stable nature of the model is obtained using the Ulam Hyers and Ulam Hyers Rassias ideas. To highlight the stability of the fractional model, the stability of solution trajectories to the disease-free and endemic steady states is graphically illustrated for the gonorrhea basic reproduction number, R0ϱ∗<1 and R0ϱ∗>1, respectively. We showed the sensitivities linked to the proposed model using the Latin hypercube sampling, singular value analysis, box plots, scatter plots, contour plots, three-dimensional plots, and sensitivity heat maps. We noticed that the transmission rate from females to males, βfm, is the most influential parameter in the spread of the disease. From the sensitivity heat maps, it is noticed that using the first four principal components analysis, the most sensitive state variables to the parameters in the model are symptomatic females, recovered males, susceptible females, and recovered females. In conjunction with the modified Adams–Bashforth method, the numerical trajectories of the fractional Caputo model are investigated. Finally, we noticed that memory changes impact the number of incubative females and incubative males.