Analysis and interpretation of a novel malaria transmission mathematical model with socioeconomic structure

Malaria is a significant threat for the human populations as it is a major source of disability and death, largely due to its environmental and socio-economic conditions. Therefore, it is crucial to modify and analyze the existing models in the literature, conduct a critical investigation, and enhance their efficacy in representing combating guidelines for disease transmission. In this study, a novel Caputo fractional derivative (CFD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {CFD}$$\end{document}) mathematical model is presented to examine the dynamics of malaria transmission within the United Kingdom (UK). Initially, the human population is categorized into two classes, namely, a highly social population and a low social population. These classes are further subdivided into two distinct categories that collectively constitute the entire human population: susceptible and infected individuals. In this analysis the seasonality in mosquito biting rate is considered to capture the disease dynamics in the UK. The fundamental characteristics of the model, such as positivity, boundedness, existence, and uniqueness, are established using fixed-point theory. The next-generation method is employed to calculate the basic reproduction number (R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}). The sensitivity of the basic reproduction numbers for both humans and mosquitoes was analyzed using Latin Hypercube Sampling and Partial Rank Correlation Coefficient with 200 runs. The local and global stability of the model disease-free equilibrium state is investigated by the construction of the Lyapunov function with LaSalle's principle. Real malaria data for the UK from 2003 to 2019 is used to estimate the crucial parameters of the model. Numerical simulations are carried out to gain insights into the factors influencing malaria transmission dynamics. The results indicate that disease progression is much higher in lower social classes compared to higher social classes. Additionally, an increase in the recruitment rate of individuals from higher social classes significantly reduces disease transmission. In conclusion, it is crucial to mobilize people and raise awareness about malaria.