Rayi Dwi Yulianti (2020) Analisis Kestabilan Dan Kontrol Optimal Pada Model Matematika Penyebaran Penyakit Menular Dengan Pengaruh Pencemaran Lingkungan. Skripsi thesis, UNIVERSITAS AIRLANGGA.

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Abstract

Infectious diseases are defined as disorders caused by viruses, bacteria, fungi or parasites. The spread of infectious diseases is one of the phenomena that can be analyzed mathematically using a mathematical model. This thesis aims to analyze the stability of the equilibrium point in the mathematical model of the spread of infectious diseases with the influence of environmental pollution, and also to apply the optimal control variables in the form of environmental sanitation efforts and media coverage. In this model, two equilibrium points are obtained, namely the non-endemic equilibrium point and the endemic equilibrium point. Local stability and the existence of equilibrium points depend on the basic reproduction number (R0). When R0<1 there is no occurrence of the spread of the disease. Meanwhile, when R0>1 the spread of infectious disease is occurred. This thesis also provides a result of an analysis of parameter sensitivity to find out which parameters that have the most significant influence on the model. The parameters which have the most significant effects are the growth rate of the pathogenic bacteria population, the death rate of the pathogenic bacteria population, and the rate recovery of infected humans. Furthermore, optimal control problems in the model are solved using Pontryagin's Maximum Principle. The results of the numerical simulation show that providing optimal control in the form of environmental sanitation and media coverage can simultaneously reduce 89,64% of the total infected human population and reduce 96,11% of the total population of pathogenic bacteria.

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