SEIR Model and Simulation for Vector Borne Diseases

ABSTRACT

An epidemic model is a simplified means of describing the transmission of infectious diseases through individuals. The modeling of infectious diseases is a tool which has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. Epidemic models are of many types. Here, SEIR model is discussed. We first discuss the basics of SEIR model. Then it is applied for vector borne diseases. Steady state conditions are derived. A threshold parameter R0 is defined and is shown that the disease will spread only if its value exceeds 1. We have applied the basic model to one specific diseases-malaria and did the sensitivity analysis too using the data for India. We found sensitivity analysis very important as it told us the most sensitive parameter to be taken care of. This makes the work more of practical use. Numerical simulation is done for vector and host which shows the population dynamics in different compartments.

Cite this paper

N. Shah and J. Gupta, "SEIR Model and Simulation for Vector Borne Diseases,"*Applied Mathematics*, Vol. 4 No. 8, 2013, pp. 13-17. doi: 10.4236/am.2013.48A003.

N. Shah and J. Gupta, "SEIR Model and Simulation for Vector Borne Diseases,"

References

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[1] J. Nedelman, “Introductory Review: Some New Thoughts about Some Old Malaria Models,” Mathematical Biosci ences, Vol. 73, No. 2, 1985, pp. 159-182. doi:10.1016/0025-5564(85)90010-0

[2] J. L. Aron, “Mathematical Modelling of Immunity to Ma laria,” Mathematical Biosciences, Vol. 90, No. 1-2, 1988, pp. 385-396. doi:10.1016/0025-5564(88)90076-4

[3] G. A. Ngwa and W. S. Shu, “Mathematical Model for En demic Malaria with Variable Human and Mosquito Po pulations,” 1999. http://www.ictp.treste.it

[4] S. A. Al-Sheikh, “Modeling and Analysis of an SEIR Epidemic Model with a Limited Resource for Treatment,” Global Journal of Science Frontier Research: Mathemat ics and Decision Sciences, Vol. 12, No. 14, 2012, pp. 57-66.

[5] P. van den Driessche and J. Watmough, “Reproduction Numbers and Sub-Threshold Endemic Equilibria for Com partmental Models of Disease Transmission,” Mathemat ics Biosciences, Vol. 180, No. 1-2, 2002, pp. 29-48. doi:10.1016/S0025-5564(02)00108-6

[6] J. H. Jones, “Notes on R0,” Stanford University, Stanford, 2007.

[7] C.-M. Dabu, “MATLAB in Biomodeling,” In: C. Ionescu, Ed., MATLAB: A Ubiquitous Tool for the Practical Engi neering, InTech, Croatia, 2011.

[8] O. Diekmann and J. A. P. Heesterbeek, “Mathematical Epi demiology of Infectious Diseases: Model Building, Ana lysis and Interpretation,” Wiley, New York, 1999.