STABILITY ANALYSIS OF THE MATHEMATICAL MODEL OF THE SPREAD OF DENGUE HEMORRHAGIC FEVER WITH THE INFLUENCE OF TREATMENT AND FOGGING

Abstract

Dengue hemorrhagic fever is an infectious disease caused by the dengue virus and transmitted by mosquito bites that has spread rapidly to all regions of the world in recent years. One of the efforts to eradicate mosquitoes that cause dengue fever is by fogging or fumigation. In addition, a treatment is also needed for dengue sufferers because there is no special drug or reliable vaccine and treatment can only be done symptomatically. In this study, a mathematical model of dengue spread will be constructed with the influence of treatment and fogging by dividing into two populations, namely humans and mosquitoes in the human population consisting of four groups, namely susceptible humans ( S_h) / Susceptible, infected humans ( I_h) / Infected, treated humans (T_h ) / Treated, cured humans (R_h ) / Recovered. The mosquito population consists of two groups, namely susceptible mosquitoes (S_h ) / Susceptible and infected mosquitoes (I_h )/ Infected. The model in this study determined disease-free and endemic equilibrium points. Next, find the basic reproduction number or  and analyze the stability of the disease-free equilibrium point obtained if R₀< 1 then the disease-free equilibrium point is asymptotic stable if all eigenvalues are negative, then the endemic equilibrium point is asymptotic stable and the last step is numerical simulation with Matlab 2017b software with parameters according to relevant references or research.

Keywords: DHF, Epidemic Model, Treatment, Fogging, Equilibrium point, Stability Analysis, Basic Reproduction Number