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All Journal Journal of Mathematical and Fundamental Sciences Communication in Biomathematical Sciences Jurnal Penelitian Perikanan Indonesia Jambura Journal of Biomathematics (JJBM) Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Matematika Integratif
Dipo Aldila
Departemen Matematika, Universitas Indonesia
Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Epidemic Dynamics with Nonlinear Incidence Considering Vaccination Effectiveness Kamalia, Putri Zahra; Aldila, Dipo
Jambura Journal of Biomathematics (JJBM) Volume 6, Issue 3: September 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v6i3.33815

Abstract

This paper presents a mathematical model that examines the effect of nonlinear incidence on disease transmission dynamics.  Furthermore, we also accommodate newborn and adult vaccination strategy as the prevention strategy to prevent rapid spread of the disease due to nonlinear incidence rate. Assuming a constant population  size,  the  system is  reduced  to  a  two-dimensions and  nondimensionalized using  the  average infectious period as the time scale.   Analytical results reveal the existence of both disease-free and endemic equilibria, with the possibility of backward bifurcation when the nonlinear incidence parameter exceeds a critical threshold.   This implies that disease persistence may still occur even when the basic reproduction number is less than one.  Numerical simulations using MATCONT conducted to visualize the occurrence of both forward and backward bifurcations phenomena.    Using COVID-19 parameter values,  a  global sensitivity analysis via Partial Rank Correlation Coefficient - Latin Hypercube Sampling method indicates that newborn vaccination has a stronger impact on reducing the basic reproduction number. These findings provide important insights for designing effective vaccination strategies and understanding the complex dynamics arising from nonlinear transmission and imperfect immunization.
Forward and Backward Bifurcation Analysis From an Imperfect Vaccine Efficacy Model With Saturated Treatment and Saturated Infection Fatahillah, Hakan Ahmad; Aldila, Dipo
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 2: December 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i2.28810

Abstract

This paper aims to study the saturation effect on the infection and recovery process within a Susceptible-Vaccination-Infected model featuring an imperfect vaccine efficacy. First, we nondimensionalized the model under the assumption of a constant population, resulting in the reduction of the model from three to two-dimensional differential equations. The analysis indicates the presence of a disease-free equilibrium (DFE) and potentially multiple endemic equilibria (EE) within the model. The calculation of the basic reproduction number further explains the model's solution conditions. In particular, we discovered that a backward bifurcation is possible under specific saturation effect values. Dulac's criterion confirmed the absence of a closed orbit in the solution region, suggesting the global stability of the endemic equilibrium when the basic reproduction number exceeds one. To supplement the analytical study, a numerical simulation was conducted to generate a bifurcation diagram, autonomous simulation, and global sensitivity analysis. The global sensitivity analysis revealed that changing the vaccination rate or recovery rate could significantly impact the basic reproduction number. Moreover, the bifurcation diagram depicting the relationship between the transmission rate and vaccination rate demonstrated that increasing the vaccination rate while maintaining the transmission rate can reduce the proportion of infected individuals within the population.
Co-Authors Aisyah Aisyah Arthana Islamilova Ashleigh Jane Hutchinson Azis, Moh. Ivan Balya, Muhammad Afief Bevina D Handari Brenda M. Samiadji Bunga Oktaviani Dewi Chukwu, Chidozie W. Dumbela, Putri A. Edy Soewono Fatahillah, Hakan Ahmad Faza Indah Lestari Gayatri Ratu Hanna Rosuliyana Hengki Tasman Husnah Samhudi Kamalia, Putri Zahra Khoshnaw, Sarbaz H. A. Latifa, Siti Leah Luis, Prisalo Matthew Woolway Muhammad Shahzad Norman Owen-Smith Peter, Olumuyiwa James Putri Zahra Kamalia Rahman, Nur Syam Ramadhan, Derio A. Sarbaz H. A. Khoshnaw Sarbaz H.A. Khosnaw Setiya Triharyuni Shahzad, Muhammad Sutrisno, Sutrisno Tama Windyhani Tamalia, Evllyn widowati widowati Zawir Rifqa Fadhlia