Journal of Applied Nonlinear Dynamics 13(1) (2024) 129--140 | DOI:10.5890/JAND.2024.03.009

D. Maheskumar$^1$, T. Jayakumar$^2$, S. Sujitha$^2$

$^1$ Department of Science and Humanities, Sri Krishna College of Technology, Coimbatore-641042, Tamil Nadu, India

$^{2}$ Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore- 641020, Tamil Nadu, India

Abstract

Controlling Dengue fever is difficult worldwide due to complex medical management settings. Therefore, such diseases should be diagnosed, and quick-acting control strategies should be used. In this article, the Mathematical Model for the system of differential equations for the spread of Dengue fever is framed and identifies the solutions to control the disease in a short period. The system consists of six equations. The first four equations represent the human population under Susceptible, Infected, Under Treatment and Recovered people (SITR Model). The vector population then comes under the categories of Susceptible and Infected Mosquitoes. In the suggested SITR Model, the identified positivity, bounded solutions, equilibrium points, stability analysis, and reproductive value are all investigated. The research results demonstrate that when the reproduction number is less than or equal to one, it is asymptotically stable (disease-free) and unstable when greater than one. In addition, confirmed a drop in mosquito bite rates, a decrease in the number of people under hospitalization and notification rates, and a rise in cure rates. The simulation on the model of SITR exposed that controlling the route of communication of this disease is necessary if we follow some strategy to restrict the transmission agent and may stop the virus from spreading further in the population.

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