Analisis Model Matematika Penyebaran Penyakit Demam Berdarah Dengue dengan Treatment

Demam Berdarah Dengue (DBD) adalah penyakit yang disebabkan oleh virus Dengue yang ditularkan ke tubuh manusia melalui gigitan nyamuk Aedes aegypti. Pasien yang terinfeksi virus memerlukan perawatan. Perawatan adalah metode yang penting dan efektif untuk mencegah dan mengendalikan penyebaran penyakit. Dalam makalah ini, kami membahas tentang analisis model matematika dari penularan demam berdarah dengan pengobatan. Studi ini meneliti model Esteva-Vargas yang dimodifikasi menggunakan pengobatan fungsi Wang. Hasil penelitian mengungkapkan bahwa ada satu kondisi kesetimbangan dari endemisitas penyakit. Jika pengobatan dilakukan dengan k<0,000186 kondisi kesetimbangan endemik penyakit stabil asimptotik, dan dalam jangka panjang akan selalu terjadi penyebaran penyakit. Sedangkan jika pengobatan dengan k≥0,000186 keadaan kesetimbangan endemik penyakit tidak stabil asimptotik, dan dalam jangka panjang akan bebas dari penyakit. Dengue Hemorrhagic Fever (DHF) is a disease caused by Dengue virus that is transmitted to human body through AedesAegypti mosquito bites. Patients infected with the virus require treatment. treatment is an important and effective method to prevent and control the spread of disease. In this paper discusses about the mathematical model analysisof transmission dengue fever with treatment.This study examined the modified Esteva-Vargas model using the treatment of the Wang function. The results obtained, there is one disease endemic equilibrium state. If the treatment with k<0,000186then diseaseendemic equilibrium state is asymptotically stable, and in the long term will always happen deployment disease. Whereas if the treatment with k≥0,000186 then diseaseendemic equilibrium state is not asymptotically stable, and in the long term will always happen freedisease.

Effect of Rainfall for the Dynamical Transmission Model of the Dengue Disease in Thailand

The SEIR (Susceptible-Exposed-Infected-Recovered) model is used to describe the transmission of dengue virus. The main contribution is determining the role of the rainfall in Thailand in the model. The transmission of dengue disease is assumed to depend on the nature of the rainfall in Thailand. We analyze the dynamic transmission of dengue disease. The stability of the solution of the model is analyzed. It is investigated by using the Routh-Hurwitz criteria. We find two equilibrium states: a disease-free state and an endemic equilibrium state. The basic reproductive number (R0) is obtained, which indicates the stability of each equilibrium state. Numerical results taking into account the rainfall are obtained and they are seen to correspond to the analytical results.

Stability analysis of the endemic equilibrium state of an infection age-structured HIV/AIDS disease pandemic

In this work we present an infection-age-structured mathematical model of AIDS disease dynamics and examine the endemic equilibrium state for stability. An explicit formula for the basic reproduction number R0 was obtained in terms of the demographic and epidemiological parameters of the model. The endemic equilibrium state was found to be locally asymptotically stable under certain conditions. Furthermore, by constructing a suitable Lyapunov functional, the endemic equilibrium state was found to be globally asymptotically stable under certain conditions prescribed on the model parameters.Keywords: Basic reproduction number, HIV/AIDS, Lyapunov functional

Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model

We present in this paper an SIRS epidemic model with saturated incidence rate and disease-inflicted mortality. The Global stability of the endemic equilibrium state is proved by constructing a Lyapunov function. For the stochastic version, the global existence and positivity of the solution is showed, and the global stability in probability and pth moment of the system is proved under suitable conditions on the intensity of the white noise perturbation.