Abstract
This paper examines the effect of treatment of Dengue fever disease. A non linear mathematical model for the problem is proposed and analysed quantitatively using the stability theory of the differential equations. The results show that the disease-free equilibrium point is locally andglobally asymptotically stable if the reproduction number (R0) is less than unity. The additive compound matrices approach is used to show that the dengue fever model’s endemic equilibrium point is locally asymptotically stable when trace, determinant and determinant of second additive compound matrix of the Jacobian matrix are all negative. However, treatment will have a control of dengue fever disease. Numerical simulation of the model is implemented to investigate the sensitivity of certain key parameters on the dengue fever disease with treatment.
Highlights
Dengue is a vector borne disease transmitted to humans by the bite of an infected female Aedes mosquito [1]
Various models have been proposed to study factors on the transmission dynamics and control the spread of dengue fever disease
We study and analyse a non linear mathematical model showing the effect of treatment on the transmission of dengue fever disease in the population
Summary
Dengue is a vector borne disease transmitted to humans by the bite of an infected female Aedes mosquito [1]. The first recognized Dengue epidemics occurred almost simultaneously in Asia, Africa, and North America in the 1780s, shortly after the identification and naming of the disease in 1779 It has spread especially in the tropical and sub tropical regions around the world, and nowadays is a disease widely found in urban and semi-urban areas, ([2]). The mathematical model of dengue transmission is a multi-population model that captures the transmission dynamics between host (human) and vector (mosquito) taking into account the four strains of dengue virus and the cross infections. No one considered a dynamical system that incorporates the effects of treatment in dengue fever disease model. We study and analyse a non linear mathematical model showing the effect of treatment on the transmission of dengue fever disease in the population
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