The Existence of a Limit-Cycle of a Discrete-Time Lotka-Volterra Model with Fear Effect and Linear Harvesting
Authors: Hasan S. Panigoro, Resmawan Resmawan, Emli Rahmi, Muhammad Afrizal Beta, Amelia Tri Rahma Sidik
Modeling the interaction between prey and predator plays an important role in maintaining the balance of the ecological system. In this paper, a discrete-time mathematical model is constructed via a forward Euler scheme, and then studied the dynamics of the model analytically and numerically. The analytical results show that the model has two fixed points, namely the origin and the interior points. The possible dynamical behaviors are shown analytically and demonstrated numerically using some phase portraits. We show numerically that the model has limit-cycles on its interior. This guarantees that there exists a condition where both prey and predator maintain their existence periodically.
E3S Web of Conferences 400, 03003 (2023)
DYNAMIC ANALYSIS OF THE MATHEMATICAL MODEL FOR THE CHOLERA DISEASE SPREAD INVOLVING MEDICATION AND ENVIRONMENTAL SANITATION
Authors: R Resmawan, Lailany Yahya, Sri Lestari Mahmud, Agusyarif Rezka Nuha, Nazrilla Hasan Laita
This study aims to analyze the mathematical model of the cholera disease spread involving medicationnd environmental sanitation. The model was analyzed by determining the equilibrium point and the basic reproduction number. The next step was to analyze the equilibrium point, sensitivity, and simulate numerically. Analysis of the stability of the disease-free and endemic equilibrium points usedhe Routh-Hurwitz criteria and the Castillo-Chaves and Song Theorem. The Analysis resultf the model produced two equilibrium points; namely the disease-freequilibrium point for local asymptotic stability and the endemic equilibrium point for local asymptotic stability if . Furthermore, the sensitivity analysis indicated the most sensitive parameters for basic reproductive number changes in succession are the parameters for natural birth rates , the transmission rate of bacteria from the environment to humans , the saturated concentration of bacteria in water , an increase in the bacterial population caused by environmental pollution rate by humans . Numerical simulations suggest an increase to give vaccine can contribute to slowing the transmission of cholera where as the reduction of a vaccine able to promote the transmission of cholera diseases.
VOL 17 NO 1 (2023): BAREKENG: JOURNAL OF MATHEMATICS AND ITS APPLICATIONS
Analisis Dinamik pada Model Matematika SVEIBR dengan Kontrol Optimal Untuk Pengendalian Penyebaran Penyakit Kolera
Authors: Agusyarif Rezka Nuha, Resmawan Resmawan, Sri Lestari Mahmud, Asriadi Asriadi, Andi Agung, Sri Istiyarti Uswatun Chasanah
Cholera is an infectious disease that attacks the human digestive system and can cause death. This article discusses the research results related to the mathematical model of the spread of cholera in the form of an optimal control system by combining three control strategies: vaccination, quarantine, and environmental sanitation. Pontryagin's maximum principle is applied to obtain optimal conditions based on the control strategy applied. Referring to the optimal conditions set, the model was solved numerically using the Runge-Kutta Order 4 method to describe the theoretical results. The calculation results show that applying the three control strategies in controlling the spread of cholera positively impacts reducing the number of cases of infection so that disease transmission can be discontinued.
Kategori
Arsip
- July 2023 (3)
- January 2023 (1)
- December 2022 (1)
- August 2022 (1)
- July 2022 (6)
- March 2022 (1)
- September 2021 (2)
- October 2020 (1)
- July 2020 (2)
- April 2020 (1)
- November 2019 (1)
- September 2019 (1)
- August 2019 (2)
- July 2019 (1)
- May 2019 (1)
- February 2019 (1)
- September 2018 (2)
- August 2018 (1)
- July 2018 (4)
- June 2018 (5)
- September 2017 (2)
- August 2017 (1)
- April 2017 (1)
- October 2016 (1)
- September 2016 (2)
- September 2015 (4)
- June 2015 (1)
Blogroll
- 01 Sistem Informasi Akademik
- 02 Repository UNG
- 03 Universitas Negeri Gorontalo
- 04 Beasiswa DIKTI
- 05 Beasiswa LPDP
- 06 BookFi
- 07 Indonesian Mathematical Society
- 08 EBSCOhost
- 09 Library Genesis
- 10 Khan Academy
- 11 Blog Pribadi
- 12 Twitter
- 13 Facebook
- 14 Pdf Drive
- 15 Pangkalan Data UNG
- 16 Differential Equation
- 17 Math is Fun
- 18 Jambura Journal of Mathematics
- 19 OSF
- 20 Sci-Hub
- 21 Researchsquare
- 22 Kalkulator Math
- 23 Gometa
- 24 Microsite
- 25 Wordwall
- 26 Science Direct
- 27 BSRE BSSN
- 28 OpenAI
- 29 Quillbot
- 30 Perplexity
- 31 Citation FInder