Mathematical analysis and optimal control of Dengue fever epidemic model

Abstract

In this article, we are working on an SEIR-SI type model for dengue disease in order to better observe the dynamics of infection in human beings. We 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}$\\mathcal{R}_{0}$\\end{document} and determine the equilibrium points. We then show the existence of global stability in each of the different states depending on the value of R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{R}_{0}$\\end{document}. Moreover, to support the theoretical work, we present numerical simulations obtained using Python. We also study the sensitivity of the parameters included in the expression of R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{R}_{0}$\\end{document} with the aim of identifying the most influential parameters in the dynamics of dengue disease spread. Finally, we introduce two functions u and v, respectively indicating the treatment of the infected people and any prevention system minimizing contact between humans and the disease causing vectors. We present the curves of the controlled system after calculating the optimal pair of controls capable of reducing the dynamics of the disease spread, still using Python.