MODELLING AND ANALYSIS OF THE VECTOR BORNE DISEASES WITH FREE LIVING PATHOGEN GROWING IN THE ENVIRONMENT


By

Aadil Hamid1 and Poonam Sinha2

1Department of mathematics, Jiwaji University, Gwalior-474011, Madhya Pradesh, India

2Department of mathematics, Govt. S.M.S. Science College, Gwalior-474009, Madhya Pradesh, India

Email:aadilhamid136@gmail.com, sinhapoonam1966@gmail.com

(Received: November 09,2021; In format : November 30, 2021; Revised in final form : March 08, 20022)


Abstract

In various infectious diseases infection is spread by vectors such as infected mosquito, black flies, ticks etc. In this paper a non-linear mathematical model is proposed and analysed for vector-borne infectious diseases like: Yellow Fever, Dengue Fever, Malaria etc. that are caused through direct transmission or through biting of an infectious vector by considering the effect of environment on the pathogen. It is further assumed that pathogen population increases with increase in discharge by human population in the environment, thereby increasing vector population. This model is analysed by using Sylvester’s criterion and by Lyapunov’s direct method. It is found that if growth of pathogen population caused by conductive human related activity increases, the spread of infectious disease increases.


2020 Mathematical Sciences Classification: 92B05, 93D05, 34D23, 34D35.

Keywords and Phrases: Vector-borne diseases, Reproduction number, Stability, Backward bifurcation



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