Russian version English version
Volume 16   Issue 2   Year 2021
Sangeeta Saha, Guruprasad Samanta

Dynamics of an Epidemic Model under the Influence of Environmental Stress

Mathematical Biology & Bioinformatics. 2021;16(2):201-243.

doi: 10.17537/2021.16.201.

References

  1. Holmes J.C. Parasites as threats to biodiversity in shrinking ecosystems. Biodivers. Conserv. 1996;5:975-983. doi: 10.1007/BF00054415
  2. Rigby M.C., More, Y. Life-history trade-offs and immune defenses. In: Evolutionary Biology of Host-Parasite Relationships: Theory Meets Reality. Eds. Poulin R., Morand S., Skorping A. Amsterdam: Elsevier Science, 2000. P. 129-142.
  3. Beck M.A., Levander O.A. Host nutritional status and its effect on a viral pathogen. J. Infect. Dis. 2000;182:S93-S96. doi: 10.1086/315918
  4. Khan R.A. Parasitism in marine fish after chronic exposure to petroleum hydrocarbons in the laboratory and to the Exxon Valdez oil spill. Bull. Environ. Contam. Toxicol. 1990;44:759-763. doi: 10.1007/BF01701799
  5. Harvell C.D., Kim K., Burkholder J.M., Colwell R.R., Epstein P.R., Grimes D.J., Hofmann E.E., Lipp E.K., Osterhaus A.D., Overstreet R.M. et al. Emerging marine diseases-climate links and anthropogenic factors. Science. 1999;285:1505-1510. doi: 10.1126/science.285.5433.1505
  6. Scott M.E. The impact of infection and disease on animal populations: implications for conservation biology. Conserv. Biol. 1980;2:40-56. doi: 10.1111/j.1523-1739.1988.tb00334.x
  7. Blanford S., Thomas M.B, Pugh C., Pell J.K. Temperature checks the Red Queen? Resistance and virulence in a fluctuating environment. Ecol. Lett. 2003;6:2-5. doi: 10.1046/j.1461-0248.2003.00387.x
  8. Dubey B. A model for the effect of pollutant on human population dependent on a resource with environmental and health policy. J. Biol. Syst. 2010;18(03):571-592. doi: 10.1142/S0218339010003378
  9. Shukla J., Agrawal A., Dubey B., Sinha P. Existence and survival of two competing species in a polluted environment: a mathematical model. J. Biol. Syst. 2001;9(02):89-103. doi: 10.1142/S0218339001000359
  10. Shukla J., Misra A., Chandra P. Mathematical modelling of the survival of a biological species in polluted water bodies. Differ. Equ. Dyn. Syst. 2007;15:209-230.
  11. Mandal P.K. Dioxin: a review of its environmental effects and its aryl hydrocarbon receptor biology. J. Comp. Physiol. B. 2005;175(4):221-230. doi: 10.1007/s00360-005-0483-3
  12. Brook R. Cardiovascular effects of air pollution. Clin. Sci. 2008;115:175-187. doi: 10.1042/CS20070444
  13. Nawahda A., Yamashita K., Ohara T., Kurokawa J., Yamaji K. Evaluation of premature mortality caused by exposure to PM2.5 and ozone in East Asia: 2000, 2005, 2020. Water Air Soil Pollut. 2012;223(6):3445-3459. doi: 10.1007/s11270-012-1123-7
  14. Pope C.A. 3rd, Burnett R.T., Thun M.J., Calle E.E., Krewski D., Ito K., Thurston G.D. Lung cancer, cardiopulmonary mortality, and long-term exposure to fine particulate air pollution. JAMA. 2002;287(9):1132-1141. doi: 10.1001/jama.287.9.1132
  15. Javan, S., Rahdar, S., Miri, M., Djahed B., Kazemian H., Fakhri Y., Eslami H., Fallahzadeh R.A., Gholizadeh A., Taghavi M. Modeling of the PM10 pollutant health effects in a semi-arid area: a case study in Zabol, Iran. Model. Earth Syst. Environ. 2021;7:455-463. doi: 10.1007/s40808-020-00874-y
  16. Laumbach R.J., Kipen H.M. Respiratory health effects of air pollution: update on biomass smoke and traffic pollution. J. Allergy Clin. Immunol. 2012;129(1):3-11. doi: 10.1016/j.jaci.2011.11.021
  17. Salvi S. Health effects of ambient air pollution in children. Paediatr. Respir. Rev. 2007;8(4):275-280. doi: 10.1016/j.prrv.2007.08.008
  18. Schell L. M., Gallo M.V., Denham M., Ravenscroft J. Effects of pollution on human growth and development: an introduction. J. Physiol. Anthropol. 2006;25(1):103-112. doi: 10.2114/jpa2.25.103
  19. van Rossem L., Rifas-Shiman S.L., Melly S.J., Kloog I., Luttmann-Gibson H., Zanobetti A., Coull B.A., Schwartz J.D., Mittleman M.A., Oken E. et al. Prenatal air pollution exposure and newborn blood pressure. Environ. Health Perspect. 2015;123(4):353-359. doi: 10.1289/ehp.1307419
  20. Schwarzman M.R., Wilson M.P. New science for chemicals policy. Science 2009;326(5956):1065. doi: 10.1126/science.1177537
  21. Richardson S.D. Disinfection by-products and other emerging contaminants in drinking water. Trends Anal. Chem. 2003;22(10):666-684. doi: 10.1016/S0165-9936(03)01003-3
  22. Hamidin N., Yu, Q.J., Connell, D.W. Human health risk assessment of chlorinated disinfection by-products in drinking water using a probabilistic approach. Water Res. 2008;42(13):3263-3274. doi: 10.1016/j.watres.2008.02.029
  23. Al-Mikhlafi A. S. Groundwater quality of yemen volcanic terrain and their geological and geochemical controls. Arab. J. Geosci. 2010;3(2):193-205. doi: 10.1007/s12517-009-0068-7
  24. Ahmad S.A., Sayed M., Barua S., Khan M.H., Faruquee M.H., Jalil A., Hadi S.A., Talukder H.K. Arsenic in drinking water and pregnancy outcomes. Environ. Health Perspect. 2001;109(6):629. doi: 10.1289/ehp.01109629
  25. Waller K., Swan S.H., DeLorenze G., Hopkins B. Trihalomethanes in drinking water and spontaneous abortion. Epidemiology. 1998;9(2):134-140. doi: 10.1097/00001648-199803000-00006
  26. Collie A.C. Pharmaceutical contaminants in potable water: potential concerns for pregnant women and children. EcoHealth. 2007;4(2):164-171. doi: 10.1007/s10393-007-0105-5
  27. Hertz-Picciotto I., Park H.Y., Dostal M., Kocan A., Trnovec T., Sram R. Prenatal exposures to persistent and non-persistent organic compounds and effects on immune system development. Basic Clin. Pharmacol. Toxicol. 2008;102(2):146-154. doi: 10.1111/j.1742-7843.2007.00190.x
  28. Grandjean P., Bellinger D., Bergman A., Cordier S., Davey-Smith G., Eskenazi B., Gee D., Gray K., Hanson M., van den Hazel P. et al. The faroes statement: human health effects of developmental exposure to chemicals in our environment. Basic Clin. Pharmacol. Toxicol. 2008;102(2):73-75. doi: 10.1111/j.1742-7843.2007.00114.x
  29. Raqib R., Ahmed S., Sultana R., Wagatsuma Y., Mondal D., Hoque A.M., Nermell B., Yunus M., Roy S., Persson L.A. et al. Effects of in utero arsenic exposure on child immunity and morbidity in rural Bangladesh. Toxicol. Lett. 2009;185(3):197-202. doi: 10.1016/j.toxlet.2009.01.001
  30. McMichael A.J., Woodruff R.E., Hales S. Climate change and human health: present and future risks. Lancet. 2006;367(9513):859-869. doi: 10.1016/S0140-6736(06)68079-3
  31. Patz J. A., Graczyk T.K., Geller N., Vittor A.Y. Effects of environmental change on emerging parasitic diseases. Int. J. Parasitol. 2000;30(12):1395-1405. doi: 10.1016/S0020-7519(00)00141-7
  32. Lipp E. K., Huq A., Colwell R.R. Effects of global climate on infectious disease: the cholera model. Clin. Microbiol. Rev. 2002;15(4):757-770. doi: 10.1128/CMR.15.4.757-770.2002
  33. Dolschak K., Gartner K., Berger T.W. The impact of rising temperatures on water balance and phenology of European beech (Fagus sylvatica L.) stands. Model. Earth Syst. Environ. 2019;5:1347-1363. doi: 10.1007/s40808-019-00602-1
  34. Stemn E., Kumi-Boateng B. Modelling of land surface temperature changes as determinant of urban heat island and risk of heat-related conditions in the Wassa West Mining Area of Ghana. Model. Earth Syst. Environ. 2020;6:1727-1740. doi: 10.1007/s40808-020-00786-x
  35. Ayub S., Akhter G., Ashraf A., Iqbal M. Snow and glacier melt runoff simulation under variable altitudes and climate scenarios in Gilgit River Basin, Karakoram region. Model. Earth Syst. Environ. 2020;6:1607-1618. doi: 10.1007/s40808-020-00777-y
  36. Devi S., Mishra R.P. A mathematical model to see the effects of increasing environmental temperature on plant–pollinator interactions. Model. Earth Syst. Environ. 2020;6:1315-1329. doi: 10.1007/s40808-020-00763-4
  37. Traore A.N., Mulaudzi K., Chari G.J., Foord S.H., Mudau L.S., Barnard T.G., Potgieter N. The impact of human activities on microbial quality of rivers in the Vhembe District, South Africa. Int. J. Environ. Res. Public Health. 2016;13(8):817. doi: 10.3390/ijerph13080817
  38. Roumagnac P., Weill F.X., Dolecek C., Baker S., Brisse S., Chinh N.T., Le T.A., Acosta C.J., Farrar J., Dougan G. et al. Evolutionary history of Salmonella typhi. Science 2006;314(5803):1301-1304. doi: 10.1126/science.1134933
  39. Riggs M.M., Sethi A.K., Zabarsky T.F., Eckstein E.C., Jump R.L., Donskey C.J. Asymptomatic Carriers Are a Potential Source for Transmission of Epidemic and Nonepidemic Clostridium difficile Strains among Long-Term Care Facility Residents. Clinical Infectious Diseases. 2007;45(8):992-998. doi: 10.1086/521854
  40. Lafferty K.D., Holt R.D. How should environmental stress affect the population dynamics of disease? Ecol. Lett. 2003;6(7):654-664. doi: 10.1046/j.1461-0248.2003.00480.x
  41. Hale J.K. Theory of functional Differential Equations. Heidelberg: Springer-Verlag, 1977. doi: 10.1007/978-1-4612-9892-2
  42. Van den Driessche P., Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 2002;180(1):29-48. doi: 10.1016/S0025-5564(02)00108-6
  43. Arriola L., Hyman J. Lecture notes on forward and adjoint sensitivity analysis with applications in Dynamical Systems, Linear Algebra and Optimisation. Mathematical and Theoretical Biology Institute, 2005.
  44. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory. Eds. Castillo-Chavez C., Blower S., van den Driessche P., Kirschner D., Yakubu A.-A. Springer, 2002. (The IMA Volumes in Mathematics and its Applications,126). doi: 10.1007/978-1-4613-0065-6
  45. LaSalle J. The stability of dynamical systems. Philadelphia: SIAM, 1976. (CBMS-NSF Regional Conference Series in Applied Mathematics). doi: 10.1137/1.9781611970432
  46. Castillo-Chavez, C., Song, B. Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 2004;1:361-404. doi: 10.3934/mbe.2004.1.361
  47. Saha S., Samanta G.P. Modelling and optimal control of HIV/AIDS prevention through PrEP and limited treatment. Physica A: Statistical Mechanics and Its Applications. 2019;516:280-307. doi: 10.1016/j.physa.2018.10.033
  48. Saha S., Samanta G.P. Dynamics of an epidemic model with impact of toxins. Physica A: Statistical Mechanics and Its Applications. 2019;527. Article No. 121152. doi: 10.1016/j.physa.2019.121152
  49. Saha S., Samanta G.P., Nieto J.J. Epidemic model of COVID-19 outbreak by inducing behavioural response in population. Nonlinear Dyn. 2020;102:455–487. doi: 10.1007/s11071-020-05896-w
  50. Gaff H., Schaefer E. Optimal control applied to vaccination and treatment strategies for various epidemiological models. Mathematical Biosciences and Engineering. 2009;6(3):469-492. doi: 10.3934/mbe.2009.6.469
  51. Kassa S., Ouhinou A. The impact of self-protective measures in the optimal interventions for controlling infectious diseases of human population. Journal of Mathematical Biology. 2015;70(1-2):213-236. doi: 10.1007/s00285-014-0761-3
  52. Joshi H., Lenhart S., Li M., Wang L. Optimal control methods applied to disease models. Contemporary Mathematics. 2006;410:187-208. doi: 10.1090/conm/410/07728
  53. Behncke H. Optimal control of deterministic epidemics. Optimal Control Applications and Methods. 2000;21(6):269-285. doi: 10.1002/oca.678
  54. Castilho, C. Optimal control of an epidemic through educational campaigns. Electronic Journal of Differential Equations. 2006;125:1-11.
  55. Hove-Musekwa S.D., Nyabadza F., Chiyaka C., Das P., Tripathi A., Mukandavire Z. Modelling and analysis of the effects of malnutrition in the spread of cholera. Math. Comput. Model. 2011;53(9):1583-1595. doi: 10.1016/j.mcm.2010.11.060
  56. Vardavas R., Blower S. The emergence of HIV transmitted resistance in Botswana: when will the WHO detection threshold be exceeded? PLoS ONE. 2007;2(1). Article No. e152. doi: 10.1371/journal.pone.0000152
  57. Donnell D., Baeten J.M., Kiarie J., Thomas K.K., Stevens W., Cohen C.R., McIntyre J., Lingappa J.R., Celum C. Heterosexual HIV-1 transmission after initiation of antiretroviral therapy: a prospective cohort analysis. Lancet. 2010;375:2092-2098. doi: 10.1016/S0140-6736(10)60705-2
  58. Collins O., Govinder K. Incorporating heterogeneity into the transmission dynamics of a waterborne disease model. J. Theor. Biol. 2014;356:133-143. doi: 10.1016/j.jtbi.2014.04.022
  59. Tien J. H., Earn D.J. Multiple transmission pathways and disease dynamics in a waterborne pathogen model. Bull. Math. Biol. 2010;72(6):1506–1533. doi: 10.1007/s11538-010-9507-6
  60. Kirk D. Optimal control theory: an introduction. Dover Publications, 2012.
  61. Coddington E., Levinson N. Theory of ordinary differential equations. Tata McGraw-Hill Education, 1955.
  62. Fleming W., Rishel R. Deterministic and stochastic optimal control. New York: Springer, 1975. (Applications of Mathematics, V. 1). doi: 10.1007/978-1-4612-6380-7_1
  63. Pontryagin L. Mathematical theory of optimal processes. CRC Press, 1987.
Table of Contents Original Article
Math. Biol. Bioinf.
2021;16(2):201-243
doi: 10.17537/2021.16.201
published in English

Abstract (eng.)
Abstract (rus.)
Full text (eng., pdf)
References

 

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