Effects of density dependent migration on the spread of infectious diseases: A Mathematical Model

• S.K. Sharma College of computer and Information Sciences, Majmaah University
• J.B. Shukla Innovative internet University for research (A think tank), Kanpur
• Jitendra Singh Department of Mathematics PPN College, CSJM University, Kanpur
• Shikha Singh Department of Mathematics PPN College, CSJM University, Kanpur

Abstract

In this paper, an SIS Mathematical model is proposed and analyzed by considering population density dependent migration. It is assumed that the disease is transmitted by direct contact of susceptibles and infectives with immigration and emigration dependent contact rate. The equilibrium analysis of the model is conducted by using the stability theory of ordinary differential equation and simulation. The model analysis shows that the spread of infectious disease increases as therate of immigration increasesbut its spread decreases as emigration rate increases and also if non-emigrating population density increases then infective population increases. The simulation study also confirms these analytical results.

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