Isi Artikel Utama
Abstrak
This study discusses the spread of diarrhea accompanied by complications resulting in death among sufferers. It is assumed that people with diarrhea can transmit the disease to susceptible individuals. Additionally, deaths occurred due to diarrhea when treatment was not administered. Individuals who have contracted diarrhea may acquire temporary immunity and then become susceptible again. The model used is SITRS. Based on the model, disease-free equilibrium points and endemic equilibrium points are obtained. The analysis was conducted around the disease-free equilibrium point, and it was concluded that the disease-free equilibrium point is locally asymptotically stable if R0<1. Furthermore, based on the simulation results, it is shown that the model's solution tends towards a disease-free equilibrium point if R0<1. . This implies that diarrhea will disappear from the population at some point if the infection level R0<1. is met.
Rincian Artikel
Hak Cipta (c) 2024 Ratna Widayati, Renal Hamim Muntoha, Umi Ma'rifah, Nita Yulianti
Artikel ini berlisensi Creative Commons Attribution 4.0 International License.
Referensi
- E. Bonyah, G. Twagirumukiza, and P. P. Gambrah, “Mathematical analysis of diarrhea model with saturated incidence rate,” Open J. Math. Sci., vol. 3(2019), no. 1, pp. 29–39, 2019, doi: 10.30538/oms2019.0046.
- H. Auld, D. MacIver, and J. Klaassen, “Heavy rainfall and waterborne disease outbreaks: The Walkerton example,” J. Toxicol. Environ. Heal. - Part A, vol. 67, no. 20–22, pp. 1879–1887, 2004, doi: 10.1080/15287390490493475.
- B. M. Gatto, L. Mari, and A. Rinaldo, “Leading Eigenvalues and the Spread of Cholera,” vol. 46, no. 7, pp. 7–8, 2013.
- A. K. Githeko, S. W. Lindsay, U. E. Confalonieri, and J. A. Patz, “Climate change and vector-borne diseases: A regional analysis,” Bull. World Health Organ., vol. 78, no. 9, pp. 1136–1147, 2000.
- J. Ardkaew and P. Tongkumchum, “Statistical modelling of childhood diarrhea in northeastern Thailand,” Southeast Asian J. Trop. Med. Public Health, vol. 40, no. 4, pp. 807–815, 2009.
- V. Astuti, Y. Yulida, and T. Thresye, “Model Matematika Penyebaran Penyakit Deare Dengan Adanya Treatment,” Epsil. J. Mat. Murni Dan Terap., vol. 15, no. 1, p. 46, 2021, doi: 10.20527/epsilon.v15i1.3152.
- S. O. Adewale, I. A. Olopade, S. O. Ajao, and G. A. Adeniran, “MATHEMATICAL ANALYSIS OF DIARRHEA IN THE PRESENCE OF VACCINE,” vol. 6, no. 12, pp. 396–404, 2015.
- A. L. Olutimo et al., “Mathematical Modeling of Diarrhea with Vaccination and Treatment Factors To cite this version : HAL Id : hal-04552022 Mathematical Modeling of Diarrhea with Vaccination and Treatment Factors,” 2024, doi: 10.9734/JAMCS/2024/v39i51891.
- E. I. Akinola, B. E. Awoyemi, I. A. Olopade, O. D. Falowo, and T. O. Akinwumi, “Mathematical Analysis of a Diarrhoea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis,” J. Appl. Sci. Environ. Manag., vol. 25, no. 7, pp. 1107–1114, 2021, doi: 10.4314/jasem.v25i7.2.
Referensi
E. Bonyah, G. Twagirumukiza, and P. P. Gambrah, “Mathematical analysis of diarrhea model with saturated incidence rate,” Open J. Math. Sci., vol. 3(2019), no. 1, pp. 29–39, 2019, doi: 10.30538/oms2019.0046.
H. Auld, D. MacIver, and J. Klaassen, “Heavy rainfall and waterborne disease outbreaks: The Walkerton example,” J. Toxicol. Environ. Heal. - Part A, vol. 67, no. 20–22, pp. 1879–1887, 2004, doi: 10.1080/15287390490493475.
B. M. Gatto, L. Mari, and A. Rinaldo, “Leading Eigenvalues and the Spread of Cholera,” vol. 46, no. 7, pp. 7–8, 2013.
A. K. Githeko, S. W. Lindsay, U. E. Confalonieri, and J. A. Patz, “Climate change and vector-borne diseases: A regional analysis,” Bull. World Health Organ., vol. 78, no. 9, pp. 1136–1147, 2000.
J. Ardkaew and P. Tongkumchum, “Statistical modelling of childhood diarrhea in northeastern Thailand,” Southeast Asian J. Trop. Med. Public Health, vol. 40, no. 4, pp. 807–815, 2009.
V. Astuti, Y. Yulida, and T. Thresye, “Model Matematika Penyebaran Penyakit Deare Dengan Adanya Treatment,” Epsil. J. Mat. Murni Dan Terap., vol. 15, no. 1, p. 46, 2021, doi: 10.20527/epsilon.v15i1.3152.
S. O. Adewale, I. A. Olopade, S. O. Ajao, and G. A. Adeniran, “MATHEMATICAL ANALYSIS OF DIARRHEA IN THE PRESENCE OF VACCINE,” vol. 6, no. 12, pp. 396–404, 2015.
A. L. Olutimo et al., “Mathematical Modeling of Diarrhea with Vaccination and Treatment Factors To cite this version : HAL Id : hal-04552022 Mathematical Modeling of Diarrhea with Vaccination and Treatment Factors,” 2024, doi: 10.9734/JAMCS/2024/v39i51891.
E. I. Akinola, B. E. Awoyemi, I. A. Olopade, O. D. Falowo, and T. O. Akinwumi, “Mathematical Analysis of a Diarrhoea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis,” J. Appl. Sci. Environ. Manag., vol. 25, no. 7, pp. 1107–1114, 2021, doi: 10.4314/jasem.v25i7.2.