Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/41470
Title: Simple epidemiology model for a non-immune disease with ordinary and resistant carriers
Other Titles: Проста епідеміологічна модель для неімунного захворювання із звичайними та резистентними збудниками
Authors: Ільницький, Г.
Ільницький, Я.
Ilnytskyi, H.
Ilnytskyi, J.
Affiliation: Львівський національний медичний університет ім. Данила Галицького
Інститут фізики конденсованих систем НАН України
Національний унівеpситет «Львівська політехніка»
Danylo Halytskyi Lviv National Medical University
Institute for Condensed Matter Physics of the Nat. Acad. Sci. of Ukraine
Lviv Polytechnic National University
Bibliographic description (Ukraine): Ilnytskyi H. Simple epidemiology model for a non-immune disease with ordinary and resistant carriers / H. Ilnytskyi, J. Ilnytskyi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 37–42.
Bibliographic description (International): Ilnytskyi H. Simple epidemiology model for a non-immune disease with ordinary and resistant carriers / H. Ilnytskyi, J. Ilnytskyi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2017. — Vol 4. — No 1. — P. 37–42.
Is part of: Mathematical Modeling and Computing, 1 (4), 2017
Issue: 1
Volume: 4
Issue Date: 15-Jun-2017
Publisher: Lviv Politechnic Publishing House
Place of the edition/event: Lviv
UDC: 004.942
[616.9-022-021484
616-036.22]
Keywords: епідеміологія
резистентні збудники
epidemiology
resistant carriers
Number of pages: 6
Page range: 37-42
Start page: 37
End page: 42
Abstract: Запропоновано модель неiмунного захворювання, яке переноситься як звичайним, так i резистентним збудниками. Ефективнiсть поширення iнфекцiї β вважається одна- ковою для обох типiв збудникiв, тодi як ефективностi лiкування γ та γ′ вiдповiдно iнфiкованих звичайним та резистентним збудником вiдрiзняється. Конверсiя звичай- ного збудника у резистентний вiдбувається iз ефективнiстю δ. Проаналiзовано ста- цiонарнi стани моделi та здiйснено переформулювання фiксованих точок у термiнах двох параметрiв, що є комбiнацiєю початкових чотирьох ефективностей. Здiйснено оцiнку нижньої та верхньої меж цих параметрiв та побудовано тривимiрний графiк фiксованих точок.
We consider the compartmental model for the non-immune disease with both ordinary and resistant carriers. The same infecting rate β is assumed for both types of carriers, whereas the curing rates γ and γ′ for the ordinary and resistant carriers, respectively, are different. The conversion from an ordinary into resistant carrier takes place with the rate δ. The stationary states for the model are evaluated and rewritten in a compact form using two reduced parameters that are combinations of initial four rates. The lower and upper bounds are given for both these parameters and the 3D plot for the fixed points is presented.
URI: http://ena.lp.edu.ua:8080/handle/ntb/41470
ISSN: 2312-9794
Copyright owner: © 2017 Lviv Polytechnic National University CMM IAPMM NASU
References (Ukraine): [1] SchwaberM. J., Navon-Venezia S., KayeK. S., Ben-AmiR., SchwartzD., CarmeliY. Clinical and Economic Impact of Bacteremia with Extended-Spectrum-Lactamase-Producing Enterobacteriaceae, Antimicrobial Agents and Chemotherapy. 50, n. 4, 1257–1262 (2006).
[2] Zapalac J. S., BillingsK.R., SchwadeN.D., RolandP. S. Suppurative Complications of Acute Otitis Media in the Era of Antibiotic Resistance. Archives of Otolaryngology–Head & Neck Surgery, 128, n. 6, 660–663 (2002).
[3] RobertsR.R., HotaB., Ahmad I., ScottR.D. I., Foster S.D., Abbasi F., Schabowski S., Kampe L.M., CiavarellaG.G., SupinoM., Naples J., CordellR., Levy S.B., WeinsteinR.A. Hospital and Societal Costs of Antimicrobial-Resistant Infections in a Chicago Teaching Hospital: Implications for Antibiotic Stewardship. Clinical Infectious Diseases. 49, n. 8, 1175–1184 (2009).
[4] FeshchenkoY., DzyublikA., PertsevaT., Bratus E., DzyublikY., GladkaG., Morrissey I., TorumkuneyD. Results from the Survey of Antibiotic Resistance (SOAR) 2011–13 in Ukraine. Journal of Antimicrobial Chemotherapy. 71, n. suppl 1, i63–i69 (2016).
[5] CohenT., DyeC., ColijnC., WilliamsB., MurrayM. Mathematical models of the epidemiology and control of drug-resistant TB. Expert Review of Respiratory Medicine. 3, n. 1, 67–79 (2009).
[6] NieuwhofG., Conington J., Bishop S.C. A genetic epidemiological model to describe resistance to an endemic bacterial disease in livestock: application to footrot in sheep. Genetics Selection Evolution. 41, n. 1, 19 (2009).
[7] ZwerlingA., Shrestha S., DowdyD.W. MathematicalModelling and Tuberculosis: Advances in Diagnostics and Novel Therapies. Advances in Medicine. 2015, 1–10 (2015).
[8] FofanaM.O., Shrestha S., KnightG.M., CohenT., WhiteR.G., Cobelens F., DowdyD.W. A Multistrain Mathematical Model To Investigate the Role of Pyrazinamide in the Emergence of Extensively Drug- Resistant Tuberculosis. Antimicrobial Agents and Chemotherapy. 61, n. 3, e00498–16 (2016).
[9] Spicknall I.H., FoxmanB., MarrsC. F., Eisenberg J.N. S. A Modeling Framework for the Evolution and Spread of Antibiotic Resistance: Literature Review and Model Categorization. American Journal of Epidemiology. 178, n. 4, 508–520 (2013).
[10] Feng Z. Applications of Epidemiological Models to Public Health Policymaking: The Role of Heterogeneity in Model Predictions. World Scientific Publishing Company (2014).
[11] Ilnytskyi J., HolovatchY., KozitskyY., IlnytskyiH. Computer simulations of a stochastic model for the non-immune disease spread. Bulletin of the National University “Lviv Polytechnic”, 800, 176–184 (2014).
[12] Ilnytskyi J., HaiduchokO., IlnytskyiH. Modelling of diaseses dissemination with multi-resistant pathogens. Computer technologies of Printing. 34, n. 2, 72–79 (2015), (in Ukrainian).
[13] IlnytskyiH., Ilnytskyi J. Modelling of dynamics and clusterisation for the spread of the diseases with multidrug resistant carriers. Scientifically Capacitant Technologies. 28, n. 4, 296–3009 (2015), (in Ukrainian).
[14] Ilnytskyi J., KozitskyY., IlnytskyiH., HaiduchokO. Stationary states and spatial patterning in anSISepidemiology model with implicit mobility. Physica A: Statistical Mechanics and its Applications. 461, 36–45 (2016).
References (International): [1] SchwaberM. J., Navon-Venezia S., KayeK. S., Ben-AmiR., SchwartzD., CarmeliY. Clinical and Economic Impact of Bacteremia with Extended-Spectrum-Lactamase-Producing Enterobacteriaceae, Antimicrobial Agents and Chemotherapy. 50, n. 4, 1257–1262 (2006).
[2] Zapalac J. S., BillingsK.R., SchwadeN.D., RolandP. S. Suppurative Complications of Acute Otitis Media in the Era of Antibiotic Resistance. Archives of Otolaryngology–Head & Neck Surgery, 128, n. 6, 660–663 (2002).
[3] RobertsR.R., HotaB., Ahmad I., ScottR.D. I., Foster S.D., Abbasi F., Schabowski S., Kampe L.M., CiavarellaG.G., SupinoM., Naples J., CordellR., Levy S.B., WeinsteinR.A. Hospital and Societal Costs of Antimicrobial-Resistant Infections in a Chicago Teaching Hospital: Implications for Antibiotic Stewardship. Clinical Infectious Diseases. 49, n. 8, 1175–1184 (2009).
[4] FeshchenkoY., DzyublikA., PertsevaT., Bratus E., DzyublikY., GladkaG., Morrissey I., TorumkuneyD. Results from the Survey of Antibiotic Resistance (SOAR) 2011–13 in Ukraine. Journal of Antimicrobial Chemotherapy. 71, n. suppl 1, i63–i69 (2016).
[5] CohenT., DyeC., ColijnC., WilliamsB., MurrayM. Mathematical models of the epidemiology and control of drug-resistant TB. Expert Review of Respiratory Medicine. 3, n. 1, 67–79 (2009).
[6] NieuwhofG., Conington J., Bishop S.C. A genetic epidemiological model to describe resistance to an endemic bacterial disease in livestock: application to footrot in sheep. Genetics Selection Evolution. 41, n. 1, 19 (2009).
[7] ZwerlingA., Shrestha S., DowdyD.W. MathematicalModelling and Tuberculosis: Advances in Diagnostics and Novel Therapies. Advances in Medicine. 2015, 1–10 (2015).
[8] FofanaM.O., Shrestha S., KnightG.M., CohenT., WhiteR.G., Cobelens F., DowdyD.W. A Multistrain Mathematical Model To Investigate the Role of Pyrazinamide in the Emergence of Extensively Drug- Resistant Tuberculosis. Antimicrobial Agents and Chemotherapy. 61, n. 3, e00498–16 (2016).
[9] Spicknall I.H., FoxmanB., MarrsC. F., Eisenberg J.N. S. A Modeling Framework for the Evolution and Spread of Antibiotic Resistance: Literature Review and Model Categorization. American Journal of Epidemiology. 178, n. 4, 508–520 (2013).
[10] Feng Z. Applications of Epidemiological Models to Public Health Policymaking: The Role of Heterogeneity in Model Predictions. World Scientific Publishing Company (2014).
[11] Ilnytskyi J., HolovatchY., KozitskyY., IlnytskyiH. Computer simulations of a stochastic model for the non-immune disease spread. Bulletin of the National University "Lviv Polytechnic", 800, 176–184 (2014).
[12] Ilnytskyi J., HaiduchokO., IlnytskyiH. Modelling of diaseses dissemination with multi-resistant pathogens. Computer technologies of Printing. 34, n. 2, 72–79 (2015), (in Ukrainian).
[13] IlnytskyiH., Ilnytskyi J. Modelling of dynamics and clusterisation for the spread of the diseases with multidrug resistant carriers. Scientifically Capacitant Technologies. 28, n. 4, 296–3009 (2015), (in Ukrainian).
[14] Ilnytskyi J., KozitskyY., IlnytskyiH., HaiduchokO. Stationary states and spatial patterning in anSISepidemiology model with implicit mobility. Physica A: Statistical Mechanics and its Applications. 461, 36–45 (2016).
Content type: Article
Appears in Collections:Mathematical Modeling And Computing. – 2017. – Vol. 4, No. 1



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