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Mathematical Model and Simulation of the Spread of COVID-19 with Vaccination, Implementation of Health Protocols, and Treatment Manaqib, Muhammad; Mahmudi, Mahmudi; Prayoga, Galuh
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.19162

Abstract

This research develops the SVEIHQR model to simulate the spread of COVID-19 with vaccination, implementation of health protocols, and treatment. The population is divided into twelve subpopulations, resulting in a mathematical model of COVID-19 in the form of a system of twelve differential equations with twelve variables. From the model, we obtain the disease-free equilibrium point, the endemic equilibrium point, and the basic reproduction number (R0). The disease-free equilibrium point is locally asymptotically stable when R0 1 and ∆5 0, where âˆ†5 is the fifth-order Routh-Hurwitz matrix of the characteristic polynomial of the Jacobian matrix. Additionally, an endemic equilibrium point exists when R0 1. The results of numerical simulations are consistent with the conducted analysis, and the sensitivity analysis reveals that the significant parameters influencing the spread of COVID-19 are the proportion of symptomatic infected individuals and the contact rate with asymptomatic infected individuals.
Model matematika penyebaran COVID-19 dengan penggunaan masker kesehatan dan karantina Manaqib, Muhammad; Fauziah, Irma; Hartati, Eti
Jambura Journal of Biomathematics (JJBM) Volume 2, Issue 2: December 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v2i2.10483

Abstract

This study developed a model for the spread of COVID-19 disease using the SIR model which was added by a health mask and quarantine for infected individuals. The population is divided into six subpopulations, namely the subpopulation susceptible without a health mask, susceptible using a health mask, infected without using a health mask, infected using a health mask, quarantine for infected individuals, and the subpopulation to recover. The results obtained two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point, and the basic reproduction number (R0). The existence of a disease-free equilibrium point is unconditional, whereas an endemic equilibrium point exists if the basic reproduction number is more than one. Stability analysis of the local asymptotically stable disease-free equilibrium point when the basic reproduction number is less than one. Furthermore, numerical simulations are carried out to provide a geometric picture related to the results that have been analyzed. The results of numerical simulations support the results of the analysis obtained. Finally, the sensitivity analysis of the basic reproduction numbers carried out obtained four parameters that dominantly affect the basic reproduction number, namely the rate of contact of susceptible individuals with infection, the rate of health mask use, the rate of health mask release, and the rate of quarantine for infected individuals.
Analysis Of Korteweg-Type Compressible Fluid Model With Slip Boundary Conditions In 3-Dimensional Half-Space Inna, Suma; Manaqib, Muhammad; Gifari, Ilman
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i2.29048

Abstract

AbstractThe Korteweg fluid model is typically used to describe the flow of two-phase fluids, where phase transitions occur at the interface, recognized by capillary effects. Korteweg extended the Navier-Stokes equations by incorporating capillarity into the equations. This article will demonstrate the solution operator for the resolvent system of the Navier-Stokes-Korteweg model with slip boundary conditions in a 3-dimensional half-space, given the coefficient condition  dengan . The steps to find the solution operator for the resolvent system include reducing the inhomogeneous resolvent system, followed by performing a partial Fourier transform on the homogeneous resolvent system to yield a simple ordinary differential equation solution.
Mathematical Modeling of HIV/AIDS Disease Spread with Public Awareness Fauziah, Irma; Manaqib, Muhammad; Zhafirah, Elisda Mieldhania
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v9i1.23424

Abstract

This study develops mathematical model for the spread of HIV/AIDS by the population is divided into seven sub-populations, namely the susceptible unaware HIV subpopulation, the susceptible aware HIV sub-population, the infected sub-population, the pre-AIDS sub-population, the ARV treatment sub-population, the AIDS sub-population, and unlikely to be infected with HIV/AIDS sub-population. In this mathematical model, two equilibrium points are obtained, namely the disease-free equilibrium point and the disease-endemic equilibrium point and the basic reproduction number . The stability analysis shows that the disease-free equilibrium point is locally asymptotically stable if  and the disease-endemic equilibrium point is locally asymptotically stable if . Numerical simulations of the equilibrium points are carried out to provide an overview of the analyzed results with parameter values from several sources. Based on the sensitivity analysis, the parameters that significantly affect the spread of HIV/AIDS are the contact rate of HIV-unaware individuals with infected individuals and the transmission rate of HIV infection