Abstract
Modelling of infectious diseases was investigated by several authors using mathematical methods. Here, we consider the model in which inhibition effect is taken into consideration in presence of delay of the infected to become infectious. In this model two equilibrium points are found, one is disease free equilibrium point and the other is the endemic equilibrium point. The endemic equilibrium point will exists under certain condition. The character of solutions in the neighbourhood of endemic equilibrium point is directly affected by inhibitory effect. The solutions in the neighbourhood of disease free equilibrium point will be asymptotically stable when the basic reproduction number less than one and the solution in the neighbourhood of endemic equilibrium point will be asymptotically stable when the basic reproduction number greater than one.
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Acknowledgments
Authors are grateful to Prof. Susmita Sarkar, Department of Applied Mathematics, University of Calcutta for her valuable guidance at every step of this work. Authors also thank the reviewer for his valuable comments which has helped to improve the paper.
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Ghosh, U., Ghosh, R. (2015). SIR Epidemic Modelling in Presence of Inhibitory Effect and Delay. In: Sarkar, S., Basu, U., De, S. (eds) Applied Mathematics. Springer Proceedings in Mathematics & Statistics, vol 146. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2547-8_22
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DOI: https://doi.org/10.1007/978-81-322-2547-8_22
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