Local Stability Analysis of Mathematical Model for Hemorrhagic Conjunctivitis Disease

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Published: Mar 30, 2018
Keywords:
Mathematical model, Hemorrhagic Conjunctivitis disease, equilibrium states, basic reproductive number.

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Sireepatch Sangsawang
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
Tareerat Tanutpanit
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
Wannissa Mumtong
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand
Puntani Pongsumpun*
Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

Abstract

Conjunctivitis is inflammation of the conjunctiva. It is commonly caused by bacteria and viruses. Allergic Conjunctivitis is distinguished by severe itching and allergen exposure. It is most commonly due to an infection or an allergic reaction. In this study, we analyzed the model for the spread of Hemorrhagic Conjunctivitis. Hemorrhagic Conjunctivitis caused by some bacteria and viruses. It can spread easily from person to person. In this model, we separate the human into susceptible, latent, infectious and recovered classes. We find the conditions for the existence of endemic and disease free equilibrium states. Also, basic reproductive number (R0), the number of secondary cases that one infected individual will cause through the duration of the infectious period, is defined and shown for qualitative behavior of the model. Numerical simulations of the model are shown by solving a system of differential equations. It shows that the endemic and disease free equilibrium are unique and stable.


Keywords: Mathematical model, Hemorrhagic Conjunctivitis disease, equilibrium states, basic reproductive number.


E-mail: [email protected]

Article Details

Issue
Vol. 12 No. 2 (2012)
Section
Original Research Articles

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