Analisis Kestabilan Model Matematika Sistem Respon Inflamasi Akibat Infeksi SARS Coronavirus

Severe Acute Respiratory Syndrome (SARS) Coronavirus infection in a human body indicated by cytokine response due to an inflammation. The purpose of this research is to construct and analyze a mathematical model of interaction between inflammatory pro-response and anti-response cytokine to predict the dynamic on inflammatory response system, so that the treatment can be optimized. The results obtained in this research describe some dynamics which happen on the cytokines, i.e. the disease-free equilibrium point is asymptotically stable when the basic reproduction number is less than one. In this condition, a patient with initial concentrations of the cytokines around the disease-free equilibrium point will be free of viral infection. The infection equilibrium point is asymptotically stable when the basic reproduction number is greater than one. In this condition, a patient with initial concentrations of the cytokines around the infection equilibrium point will be infected by the virus. Probability of a patient being free of viral infection can increase if the production rate of the cytokines are decreased or the degradation rate of the cytokines are increased.Infeksi Severe Acute Respiratory Syndrome (SARS) Coronavirus pada tubuh manusia ditandai dengan respon sitokin akibat adanya inflamasi. Pada artikel ini, dikonstruksi model matematika interaksi antara sitokin pro-respon dan anti-respon inflamasi untuk memprediksi dinamika pada sistem respon inflamasi, sehingga pengobatan dapat dioptimalkan. Titik ekuilibrium bebas penyakit bersifat stabil asimtotik jika bilangan reproduksi dasar bernilai kurang dari satu. Pada kondisi ini, pasien dengan keadaan awal konsentrasi sitokin pro-respon dan anti-respon inflamasi di sekitar titik ekuilibrium bebas penyakit akan bebas dari infeksi virus. Titik ekuilibrium infeksi bersifat stabil asimtotik jika bilangan reproduksi dasar bernilai lebih dari satu. Pada kondisi ini, pasien dengan keadaan awal konsentrasi sitokin pro-respon dan anti-respon inflamasi di sekitar titik ekuilibrium infeksi akan terinfeksi virus. Probabilitas terbebasnya pasien dari infeksi virus dapat bertambah apabila tingkat produksi konsentrasi pro-respon dan anti-respon sitokin menurun atau tingkat degradasi sitokin pro-respon dan anti-respon meningkat

GLOBAL STABILITY OF DISEASE-FREE EQUILIBRIA IN COVID-19 SPREAD THROUGH LIVING AND INANIMATE OBJECTS MATHEMATICAL MODEL

Covid-19 is a dangerous disease that is easily transmitted, both through living media in the form of interactions with infected human, as well as through inanimate objects in the form of surfaces contaminated with the Coronavirus. Various preventive and repressive efforts have been made to prevent the spread of this disease, such as isolating and recovering the infected human. In this study, the authors construct and analyze a new mathematical model in the form of a three-dimensional differential equations system that represent the interactions between subpopulations of coronavirus living on inanimate objects, susceptible human, and infected human within a population. The purpose of this study is to investigate the criteria that must be met in order to create a population free from Covid-19 by considering inanimate objects as a medium for its spread besides living objects. The model solution that represents the number of each subpopulation is non-negative and bounded, so it is in accordance with the biological condition that the number of subpopulations cannot be negative and there is always a limit for its value. The eradication rate of Coronavirus living on inanimate objects, the recovery rate of infected human, and the interaction rate between susceptible human and infected human such that the population is free from Covid-19 for any initial conditions of each subpopulation were investigated in this study through global stability analysis of the disease-free equilibrium point of the model

Global stability of latency equilibria on mathematical model for human inflammatory response to coronavirus infection

Latent phase of Coronavirus infection is a period of time in which an infected person is noninfectious and asymptomatic, so that it does not have a high risk of transmission. We construct a mathematical model that describes human inflammatory response system, i.e. interaction between pro-inflammatory and anti-inflammatory cytokine during Coronavirus infection to identify the sufficient condition for global stability of latency equilibria of the model, so that the latency period of an infected person can be maintained and transmission of Coronavirus can be prevented. The model is a three-dimensional differential equation system that has an equilibria that represents the latent phase of Coronavirus infection. The latency equilibria is globally asymptotically stable if the maximum concentration of Coronavirus is less than the ratio between the natural degradation of pro-inflammatory cytokine and the increasing rate of pro-inflammatory cytokine concentration caused by Coronavirus. Fulfillment of the sufficient condition to create a globally asymptotically stable latency equilibria results in Coronavirus infection on the infected person will remain in latent phase, so that Coronavirus transmission can be suppressed

Mudah dan menyenangkan mengolah data dengan spss statistika 26

Pembahasan dimulai dari statistika, deskriptif, seperti penggambaran data secara grafik dan numerik.viii, 216 hlm, 21,1 x 14 c

Mudah dan menyenangkan mengolah data dengan spss statistika 26

Pembahasan dimulai dari statistika, deskriptif, seperti penggambaran data secara grafik dan numerik.viii, 216 hlm, 21,1 x 14 c