AbstrakInfeksi Hepatitis B terus berlanjut menjadi masalah kesehatan global. Termotivasi hal tersebut, kami memperkenalkan model matematika infeksi virus Hepatitis B (VHB). Berangkat dari fakta bahwa tingkat infeksi bilinear tidak selalu benar dalam menggambarkan interaksi virus dengan sel rentan di kehidupan nyata, maka digunakan tingkat infeksi nonlinear pada model. Fase adsorpsi dalam proses infeksi virus dipertimbangkan dalam model sebagai salah satu penyebab penurunan populasi partikel virus. Pada model, populasi partikel virus dibagi menjadi dua kompartemen yaitu, virion dan kapsid intraseluler yang mengandung DNA-VHB. Populasi sel dibagi menjadi dua kompartemen yaitu, sel rentan dan sel terinfeksi. Perilaku dinamik model dianalisis dengan menentukan titik kesetimbangan bebas infeksi dan endemik, bilangan reproduksi dasar, serta kestabilan lokal dari titik kesetimbangan tersebut. Hasil analisis dan simulasi numerik menunjukkan bahwa stabilitas titik kesetimbangan bebas infeksi maupun endemik bergantung pada bilangan reproduksi dasar. Kata kunci: adsorpsi, analisis dinamik, bilangan reproduksi dasar, model matematika, virus Hepatitis B. AbstractHepatitis B infection continues to be a global health problem. Motivated with this, we introduce a mathematical model of hepatitis B virus infection (HBV). Based on the fact that bilinear infection rate is not always true in describing viral interactions with susceptible cells in real life, we use nonlinear infection rate on the model. The adsorption phase in the viral infection process is considered in the model as one of the causes of the population decline in viral particles. In the model, the viral particle population is divided into two compartments:, virions and intracellular capsid containing HBV-DNA. Cell population is divided into two compartments: susceptible cells and infected cells. The dynamic behavior of the model is analyzed by determining the free-infection equilibrium point and endemic equilibrium point, the basic reproduction number, and the local stability of the equilibrium points. The analysis and numerical simulation results show that the stability of the equilibriia, free-infection or endemic, depend on the basic reproduction number.
In this paper, a model for characterizing the dynamics of vector-borne diseases is put out, emphasizing Japanese encephalitis. The susceptible-infectious-recovered (SIR) model for the host population and the susceptible-infectious (SI) model for the vector and reservoir populations are used to examine the role of host-vector-reservoir dynamics and their interplay. The standard incidence rate represents the probability of an actual disease contact. The model has two equilibrium points: an endemic equilibrium point that only exists under specific circumstances and a disease-free equilibrium point that always exists. The stability analysis of the model’s equilibrium point has been established. The basic reproduction number is calculated using the next-generation matrix method. A sensitivity analysis on models supported by numerical simulations is provided to demonstrate the critical parameter that affects the spread of disease. Our findings indicate that vector-reservoir transmission is the primary cause of endemic. Controlling vector-reservoir transmission lowers the likelihood of human infection and creates disease-free settings.
Infeksi Hepatitis B terus berlanjut menjadi masalah kesehatan global. Termotivasi hal tersebut, kami memperkenalkan model matematika infeksi virus Hepatitis B (VHB). Berangkat dari fakta bahwa tingkat infeksi bilinear tidak selalu benar dalam menggambarkan interaksi virus dengan sel rentan di kehidupan nyata, maka digunakan tingkat infeksi nonlinear pada model. Fase adsorpsi dalam proses infeksi virus dipertimbangkan dalam model sebagai salah satu penyebab penurunan populasi partikel virus. Pada model, populasi partikel virus dibagi menjadi dua kompartemen yaitu, virion dan kapsid intraseluler yang mengandung DNA-VHB. Populasi sel dibagi menjadi dua kompartemen yaitu, sel rentan dan sel terinfeksi. Perilaku dinamik model dianalisis dengan menentukan titik kesetimbangan bebas infeksi dan endemik, bilangan reproduksi dasar, serta kestabilan lokal dari titik kesetimbangan tersebut. Hasil analisis dan simulasi numerik menunjukkan bahwa stabilitas titik kesetimbangan bebas infeksi maupun endemik bergantung pada bilangan reproduksi dasar. Kata kunci: adsorpsi, analisis dinamik, bilangan reproduksi dasar, model matematika, virus Hepatitis B.
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