Education and Mathematics Models (A Case Study of Epidemiology of Virus Spread)
DOI:
https://doi.org/10.51278/bse.v3i3.940Keywords:
Education Models, Mathematics Models, SIS (Susceptible, Infected, Susceptible)Abstract
Viruses are the cause of diseases that affect the human body and can lead to pandemics and epidemics in various countries. No new content has been added beyond the original text. Viruses are the cause of diseases that affect the human body and can lead to pandemics and epidemics in various countries. The language used is clear, objective, and value-neutral, with a formal register and precise word choice. The text adheres to conventional structure and format, with consistent citation and footnote style. The text is free from grammatical errors, spelling mistakes, and punctuation errors. The purpose of this research is to determine the SIS model for the spread of viral diseases, such as Covid-19 and bird flu, and their resolution behavior. The model is formed by creating a flow diagram of the disease spread using the SIS (Susceptible, Infected, Susceptible) model. The sentences and paragraphs create a logical flow of information with causal connections between statements. The study revealed two equilibrium points: the disease-free equilibrium point and the endemic equilibrium point. To analyze the stability of the disease-free equilibrium point, linearization around the equilibrium point was used. The disease-free equilibrium point is asymptotically stable if the basic reproduction number is less than one, indicating that the disease will disappear after a certain period of time. Numerical simulations were conducted to analyze the behavior of the disease model.
Keywords: Education Models, Mathematics Models, SIS (Susceptible, Infected, Susceptible)
References
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Harraq, Jamal & Hattaf, Khalid & Achtaich, Naceur. (2020). Epidemiological models in high school mathematics education. Communications in Mathematical Biology and Neuroscience. 10.28919/cmbn/4708.
Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Rev. 42, 599–653. doi: 10.1137/S0036144500371907
Kumar, N., Sharma, S., Barua, S., Tripathi, B. N., and Rouse, B. T. (2018). Virological and immunological outcomes of coinfections. Clin. Microbiol. Rev. 31, e00111-17. doi: 10.1128/CMR.00111-17
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Nickbakhsh, S., Mair, C., Matthews, L., Reeve, R., Johnson, P. C., Thorburn, F., et al. (2019). Virus-virus interactions impact the population dynamics of influenza and the common cold. Proc. Natl. Acad. Sci. U.S.A. 116, 27142–27150. doi: 10.1073/pnas.1911083116
Pascalis, H., Temmam, S., Turpin, M., Rollot, O., Flahault, A., Carrat, F., et al. (2012). Intense co-circulation of non-influenza respiratory viruses during the first wave of pandemic influenza pH1N1/2009: a cohort study in Reunion Island. PLoS ONE 7, e44755. doi: 10.1371/journal.pone.0044755
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Stowe, J., Tessier, E., Zhao, H., Guy, R., Muller-Pebody, B., Zambon, M., et al. (2021). Interactions between SARS-CoV-2 and influenza, and the impact of coinfection on disease severity: a test-negative design. Int. J. Epidemiol. 50, 1124–1133. doi: 10.1093/ije/dyab081
Sun, Y., Zhu, R., Zhao, L., Deng, J., Wang, F., Ding, Y., et al. (2014). Effect of human rhinovirus infection in pediatric patients with influenza-like illness on the 2009 pandemic influenza A(H1N1) virus. Chin. Med. J. 127, 1656–1660. doi: 10.3760/cma.j.issn.0366-6999.20132386
Vytla, Vishnu, et al. (2021), Mathematical Models for Predicting Covid-19 Pandemic: A Review. Journal of Physics: Conference Series ; Bristol Vol. 1797, Iss. 1, (Feb 2021). DOI:10.1088/1742-6596/1797/1/012009
Whitakerdowling, P., and Youngner, J. (1987). Viral interference-dominance of mutant viruses over wild-type virus in mixed infections. Microbiol. Rev. 51, 179–191. doi: 10.1128/MMBR.51.2.179-191.1987
Zakharov, Victor, Yulia Balykina, Igor Ilin, and Andrea Tick. 2022. "Forecasting a New Type of Virus Spread: A Case Study of COVID-19 with Stochastic Parameters" Mathematics 10, no. 20: 3725. https://doi.org/10.3390/math10203725
.
Ackerman, E., Longini, I., Seaholm, S., and Hedin, A. (1990). Simulation of mechanisms of viral interference in influenza. Int. J. Epidemiol. 19, 444–454. doi: 10.1093/ije/19.2.444
Ackleh, A., and Allen, L. (2005). Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density-dependent host mortality. Discr. Cont. Dyn. Syst. B 5, 175–188. doi: 10.3934/dcdsb.2005.5.175
Adekola HA, Adekunle IA, Egberongbe HO, Onitilo SA, Abdullahi IN, 2020, Mathematical modeling for infectious viral disease: The COVID-19
perspective. J Public Affairs ;20:e2306. https://doi.org/
10.1002/pa.2306
Alemzewde Ayalew,Yezbalem Molla,Tenaw Tilahun, and Tadele Tesfa, 2022, Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control. Journal of Applied Mathematics, https://doi.org/10.1155/2023/8570311
Ali Yousef, et al. (2023) A mathematical model of COVID-19 and the multi fears of the community during the epidemiological stage. Journal of Computational and Applied Mathematics, Volume 419, 114624. https://doi.org/10.1016/j.cam.2022.114624.
Almaraz, E., and Gomez-Corral, A. (2019). Number of infections suffered by a focal individual in a two-strain SIS model with partial cross-immunity. Math. Methods Appl. Sci. 42, 4318–4330. doi: 10.1002/mma.5652
Alosaimi, B., Naeem, A., Hamed, M. E., Alkadi, H. S., Alanazi, T., Al Rehily, S. S., et al. (2021). Influenza co-infection associated with severity and mortality in COVID-19 patients. Virol. J. 18, 127. doi: 10.1186/s12985-021-01 594-0
Al-Sadeq, D. W., and Nasrallah, G. K. (2020). The incidence of the novel coronavirus SARS-CoV-2 among asymptomatic patients: a systematic review. Int. J. Infect. Dis. 98, 372–380. doi: 10.1016/j.ijid.2020.06.098
Amador, J., Armesto, D., and Gomez-Corral, A. (2019). Extreme values in SIR epidemic models with two strains and cross-immunity. Math. Biosci. Eng. 16, 1992–2022. doi: 10.3934/mbe.2019098
Amato, M., Werba, J. P., Frigerio, B., Coggi, D., Sansaro, D., Ravani, A., et al. (2020). Relationship between influenza vaccination coverage rate and COVID-19 outbreak: an italian ecological study. Vaccines 8, 535. doi: 10.3390/vaccines8030535
Anderson, R. M., Heesterbeek, H., Klinkenberg, D., and Hollingsworth, T. D. (2020). How will country-based mitigation measures influence the course of the covid-19 epidemic? Lancet 395, 931–934. doi: 10.1016/S0140-6736(20)30 567-5
Andreason, V. (2018). Epidemics in competition: partial cross-immunity. Bull. Math. Biol. 80, 2957–2977. doi: 10.1007/s11538-018-0495-2
Anestad, G. (1982). Interference between outbreaks of respiratory syncytial virus and influenza virus infection. Lancet 1:502. doi: 10.1016/s0140-6736(82)91466-0
Anestad, G., and Nardbo, S. A. (2009). Interference between outbreaks of respiratory viruses. 1Euro Surveil. 14, 19359. doi: 10.2807/ese.14.41.19359-en
B. Ivorra, M.R. Ferrández, M. Vela-Pérez, A.M. Ramos, 2020, Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China, Communications in Nonlinear Science and Numerical Simulation, Volume 88, 105303. https://doi.org/10.1016/j.cnsns.2020.105303.
Choe, Y. J., Smit, M. A., and Mermel, L. A. (2019). Seasonality of respiratory viruses and bacterial pathogens. Antimicrob. Resist. Infect. Control 8, 125. doi: 10.1186/s13756-019-0574-7
Cui, J., Zhang, Y., Feng, Z., Guo, S., and Zhang, Y. (2019). Influence of asymptomatic infections for the effectiveness of facemasks during pandemic influenza. Math. Biosci. Eng. 16, 3936–3946. doi: 10.3934/mbe.2019194
Hamou, A.A., Rasul, R.R.Q., Hammouch, Z. et al. 2022. Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco. Comp. Appl. Math. 41, 289. https://doi.org/10.1007/s40314-022-01990-4
Harraq, Jamal & Hattaf, Khalid & Achtaich, Naceur. (2020). Epidemiological models in high school mathematics education. Communications in Mathematical Biology and Neuroscience. 10.28919/cmbn/4708.
Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Rev. 42, 599–653. doi: 10.1137/S0036144500371907
Kumar, N., Sharma, S., Barua, S., Tripathi, B. N., and Rouse, B. T. (2018). Virological and immunological outcomes of coinfections. Clin. Microbiol. Rev. 31, e00111-17. doi: 10.1128/CMR.00111-17
Mair, C., Nickbakhsh, S., Reeve, R., McMenamin, J., Reynolds, A., Gunson, R. N., et al. (2019). Estimation of temporal covariances in pathogen dynamics using Bayesian multivariate autoregressive models. PLoS Comput. Biol. 15, e1007492. doi: 10.1371/journal.pcbi.1007492
Nickbakhsh, S., Mair, C., Matthews, L., Reeve, R., Johnson, P. C., Thorburn, F., et al. (2019). Virus-virus interactions impact the population dynamics of influenza and the common cold. Proc. Natl. Acad. Sci. U.S.A. 116, 27142–27150. doi: 10.1073/pnas.1911083116
Pascalis, H., Temmam, S., Turpin, M., Rollot, O., Flahault, A., Carrat, F., et al. (2012). Intense co-circulation of non-influenza respiratory viruses during the first wave of pandemic influenza pH1N1/2009: a cohort study in Reunion Island. PLoS ONE 7, e44755. doi: 10.1371/journal.pone.0044755
Pinky Lubna, Dobrovolny Hana M. 2022, Epidemiological Consequences of Viral Interference: A Mathematical Modeling Study of Two Interacting Viruses. Frontiers in Microbiology Vol.13, DOI: 10.3389/fmicb.2022.830423
Salihu Sabiu Musa, et al. (2021), Mathematical modeling of COVID-19 epidemic with effect of awareness programs. Infectious Disease Modelling, Volume 6, Pages 448-460, https://doi.org/10.1016/j.idm.2021.01.012
Stowe, J., Tessier, E., Zhao, H., Guy, R., Muller-Pebody, B., Zambon, M., et al. (2021). Interactions between SARS-CoV-2 and influenza, and the impact of coinfection on disease severity: a test-negative design. Int. J. Epidemiol. 50, 1124–1133. doi: 10.1093/ije/dyab081
Sun, Y., Zhu, R., Zhao, L., Deng, J., Wang, F., Ding, Y., et al. (2014). Effect of human rhinovirus infection in pediatric patients with influenza-like illness on the 2009 pandemic influenza A(H1N1) virus. Chin. Med. J. 127, 1656–1660. doi: 10.3760/cma.j.issn.0366-6999.20132386
Vytla, Vishnu, et al. (2021), Mathematical Models for Predicting Covid-19 Pandemic: A Review. Journal of Physics: Conference Series ; Bristol Vol. 1797, Iss. 1, (Feb 2021). DOI:10.1088/1742-6596/1797/1/012009
Whitakerdowling, P., and Youngner, J. (1987). Viral interference-dominance of mutant viruses over wild-type virus in mixed infections. Microbiol. Rev. 51, 179–191. doi: 10.1128/MMBR.51.2.179-191.1987
Zakharov, Victor, Yulia Balykina, Igor Ilin, and Andrea Tick. 2022. "Forecasting a New Type of Virus Spread: A Case Study of COVID-19 with Stochastic Parameters" Mathematics 10, no. 20: 3725. https://doi.org/10.3390/math10203725
.
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Published
2023-12-29
How to Cite
Peranginangin, A. P. (2023). Education and Mathematics Models (A Case Study of Epidemiology of Virus Spread). Bulletin of Science Education, 3(3), 330–347. https://doi.org/10.51278/bse.v3i3.940
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