KESTABILAN LOKAL TITIK EKUILIBRIUM MODEL PENYEBARAN PENYAKIT POLIO

Authors

DOI:

https://doi.org/10.25077/jmua.12.2.153-167.2023

Keywords:

Polio Dynamics, Polio Model, Numerical Simulation

Abstract

The fact shows that polio is very dangerous to humanity, it is necessary to study the dynamics of the spread of polio. One way, namely a mathematical approach in the form of a mathematical model for the spread of polio. The mathematical model used in this study is the SEIV model. This study aims to provide a description of the dynamics of the spread of polio. The results of this study are expected to be used as a reference to study the dynamics of the spread of polio in an area. The method used in the implementation of this research is literature study. The first stage starts with the model formulation. The second stage analyzes the model that has been formed and the last one makes a model simulation. The formed SEIV model is a system of nonlinear differential equations. The basic reproduction number  parameter is obtained from the analysis of the system. If the basic reproduction number less than one, then there is a single point of  free disease equilibrium that is locally stable asymptotically. Conversely, if the basic reproduction number more than one, then there are two points of equilibrium, namely the point of free equilibrium of disease  and the endemic equilibrium point . When the basic reproduction number more than one endemic equilibrium point  is stable asymptotically locally. Based on the simulation, if  the basic reproduction number less than one for t → ∞ and value (S, E, I, V) are close enough to E*, the system solution will move to E*. This means that if the basic reproduction number less than one, the disease will not be endemic and tends to disappear in an infinite amount of time. Conversely, if the basic reproduction number more than one for t → ∞ and the value (S, E, I, V) are close enough to E^, then the system solution will move towards E^. This means that if the basic reproduction number more than one, then the disease will remain in the population but not reach extinction in an infinite amount of time

Author Biographies

Joko Harianto, Universitas Cenderawasih

Department of Mathematics

Venthy Angelika, Universitas Cenderawasih

Prodi Sarjana Kedokteran Fakultas Kedokteran

Feby Seru, Universitas Cenderawasih

Department of Mathematics

References

W. O. Kermack and A. G. McKendrick, “Contributions to the mathematical theory of epidemics-I,†Bull. Math. Biol., 1991.

M. Agarwal and A. S. Bhadauria, “Modeling Spread of Polio with the Role of Vaccination,†Appl. Appl. Math. An Int. J. MSC, vol. 6, no. 2, 2011.

M. Naveed, D. Baleanu, A. Raza, M. Rafiq, and A. H. Soori, “Treatment of polio delayed epidemic model via computer simulations,†Comput. Mater. Contin., vol. 70, no. 2, 2022.

M. Naveed, D. Baleanu, M. Rafiq, A. Raza, A. H. Soori, and N. Ahmed, “Dynamical behavior and sensitivity analysis of a delayed coronavirus epidemic model,†Comput. Mater. Contin., vol. 65, no. 1, 2020.

T. Hussain, M. Ozair, M. Faizan, S. Jameel, and K. S. Nisar, “Optimal control approach based on sensitivity analysis to retrench the pine wilt disease,†Eur. Phys. J. Plus, vol. 136, no. 7, 2021.

A. Raza, M. Rafiq, N. Ahmed, I. Khan, K. S. Nisar, and Z. Iqbal, “A structure preserving numerical method for solution of stochastic epidemic model of smoking dynamics,†Comput. Mater. Contin., vol. 65, no. 1, 2020.

P. Kumar, V. S. Erturk, H. Abboubakar, and K. S. Nisar, “Prediction studies of the epidemic peak of coronavirus disease in Brazil via new generalised Caputo type fractional derivatives,†Alexandria Eng. J., vol. 60, no. 3, 2021.

Z. Ul Abadin Zafar, H. Rezazadeh, M. Inc, K. S. Nisar, T. A. Sulaiman, and A. Yusuf, “Fractional order heroin epidemic dynamics,†Alexandria Eng. J., vol. 60, no. 6, 2021.

M. S. Arif, A. Raza, K. Abodayeh, M. Rafiq, M. Bibi, and A. Nazeer, “A numerical efficient technique for the solution of susceptible infected recovered epidemic model,†C. - Comput. Model. Eng. Sci., vol. 124, no. 2, 2020.

A. Raza et al., “Numerical treatment for stochastic computer virus model,†C. - Comput. Model. Eng. Sci., vol. 120, no. 2, 2019.

W. Shatanawi, A. Raza, M. S. Arif, M. Rafiq, M. Bibi, and M. Mohsin, “Essential features preserving dynamics of stochastic dengue model,†C. - Comput. Model. Eng. Sci., vol. 126, no. 1, 2021.

T. A. Biala and A. Q. M. Khaliq, “A fractional-order compartmental model for the spread of the COVID-19 pandemic,†Commun. Nonlinear Sci. Numer. Simul., vol. 98, 2021.

K. M. Furati, I. O. Sarumi, and A. Q. M. Khaliq, “Fractional model for the spread of COVID-19 subject to government intervention and public perception,†Appl. Math. Model., vol. 95, 2021.

A. M. S. Mahdy, N. H. Sweilam, and M. Higazy, “Approximate solution for solving nonlinear fractional order smoking model,†Alexandria Eng. J., vol. 59, no. 2, 2020.

A. M. S. Mahdy, K. Lotfy, W. Hassan, and A. A. El-Bary, “Analytical solution of magneto-photothermal theory during variable thermal conductivity of a semiconductor material due to pulse heat flux and volumetric heat source,†Waves in Random and Complex Media, vol. 31, no. 6, 2021.

Y. A. Amer, A. M. S. Mahdy, and H. A. R. Namoos, “Reduced differential transform method for solving fractional-order biological systems,†J. Eng. Appl. Sci., vol. 13, no. 20, 2018.

X. Liu et al., “FRACTIONAL MATHEMATICAL MODELING TO THE SPREAD OF POLIO WITH THE ROLE OF VACCINATION UNDER NON-SINGULAR KERNEL,†Fractals, vol. 30, no. 5, 2022.

Y. C. Umam, M. Kharis, and Supriyono, “Model Epidemi SEIV Penyebaran Penyakit Polio pada Populasi Tak-Konstan,†Unnes J. Math., vol. 5, no. 2, 2016.

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Published

03-02-2024

Issue

Vol. 12 No. 2 (2023)

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