MATHEMATICAL MODEL OF TIPHOID FEVER SPREAD USING SATURATED INCIDENCE RATE
Abstract
Typhoid fever is a bacterial infectious disease caused by Salmonella typhi, transmitted through food or water contaminated by feces or urine of people whowas infected by Salmonella typhi. In this research, mathematical model of typhoid fever with saturated incidence rate that when infected population increase, people more aware and inhibit the spread of the disease. According to model analysis, there was two equilibrium point, free disease and endemic. The basic reproduction number has been computed using next-generation matrix method. We have shown that the disease free equilibrium point of the model is globally asymptotic stable when basic reproduction number is less than unity and endemic equilibrium point is locally asymptotic stable when basic reproduction number is greater than unity. Numerical simulation was shown around equilibrium point. The addition of the saturated incidence rate inhibits the spread of typhoid. When the basic reproduction number is less than 1, typhoid will disappear and if the basic reproduction number is greater than 1, typhoid will remain.
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Anton, H., Rorres, C., 2005, Elementary Linear Algebra 9th Edition, New Jersey: John Wiley & Sons, Inc.
Castillo-Chaves, C., Feng., Huang, W. 2002, On the Computation of R0 and its Role on Global Stability, Mathematical Approaches for Emerging and Reemerging, New York: Springer.
Castillo-Chaves, C., dan Brauer, F., 2010, Mathematical Models in Population Biology and Epidemiology, New York: Springer.
Deris, Z., dkk., 2010, Relapse of Typhoid Fever in North-eastern state in Malaysia, Asian Tropical Medicine Journal (Elsevier), pp 48-50.
Edward, S., Nkuba, N., 2016, Modelling Typhoid Fever with Education, Vaccination and Treatment, Engineering Mathematics Vol. 1, No. 1, pp. 44-52.
Murray, J.D., 1993, Mathematical Biology, Berlin: Springer-Verlag.
Mushayabasa, S., 2012, “A Simple Epidemiological Model for Typhoid with Saturated Incidence Rate and Treatment Effect, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Vol:6, No:6.
Sorrell, T. et al.,2015, Typhoid Fever cases in the U. S. Militaryâ€, BMC Infectious Disease, pp 15:424.
Wiggin, S.,2000, Introduction to Applied Nonlinear Dynamical Systems and Chaos 2th, New York: Springer.
WHO, 2003, Background document: The diagnosis, treatmen and prevention of typhoid fever, tersedia http://www.who.int/rpc/TFGuideWHO.pdf diakses tanggal 14 Maret 2021.
DOI: http://dx.doi.org/10.12928/admathedu.v11i2.20482
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