MATHEMATICAL MODEL OF TIPHOID FEVER SPREAD USING SATURATED INCIDENCE RATE
DOI:
https://doi.org/10.12928/admathedu.v11i2.20482Keywords:
typhoid fever, mathematical model, saturated incidence rate, equilibrium point, basic reproduction number.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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