Abstract
Two model systems are proposed and analyzed. In the first system the disease transmission in the population is considered to be purely horizontal, while in the second system the transmission is considered to be mixed, i.e., both horizontal and vertical transmissions are present in the system. Analytically both the systems are analyzed separately and then numerical simulations are performed to observe the effect of disease transmission in disease dynamics. Our results showed that the presence of vertical transmission along with the horizontal transmission increases the virulence of the pathogens.
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References
Mansfield BE, Dionne MS, Schneider DS, Freitag NE (2003) Exploration of host–pathogen interactions using Listeria monocytogenes and Drosophila melanogaster. Cell Microbiol 5:901–911
Ross R (1916) An application of theory of probabilities to the study of a priori pathometry. Part I. Proc R Soc Lond Ser A 92:204–230
Ross R, Hudson HP (1917) An application of theory of probabilities to the study of a priori pathometry. Part II and part III. Proc R Soc Lond Ser A 93:212–240
Roy PK, Chattopadhyay B (2010) Host pathogen interactions with recovery rate: a mathematical study. In: Lecture notes in engineering and computer science: proceedings of the World Congress on engineering 2010, WCE 2010, 30 June–2 July, London, UK, pp 521–526
Anderson RM, May RM (1981) The population dynamics of microparasites and their invertebrate hosts. Philos Trans R Soc Lond B 291:451–524
Anderson RM, May RM (1991) Infectious diseases of humans, dynamics and control. Oxford Science Publications, Oxford
Begon M, Bowers RG (1995) Host–host pathogen models and microbial pest control: the effect of host self regulation. J Theor Biol 169:275–287
Holt RD, Pickering J (1985) Infectious disease and species coexistence: a model in Lotka–Volterra form. Am Nat 126:196–211
Kribs-Zaleta CM, Velasco-Hernandez JX (2000) A simple vaccination model with multiple endemic states. Math Biosci 164(2):183–201
Moghadas SM (2004) Modelling the effect of imperfect vaccines on disease epidemiology. Discrete Continuous Dyn Syst Ser B 4(4):999–1012
Brankston G, Gitterman L, Hirji Z, Lemieux C, Gardam M (2007) Transmission of influenza A in human beings. Lancet Infect Dis 7:257–265
Attye A, Auger P, Joly J (1990) Incidence of occult athlete’s foot in swimmers. Eur J Epidemiol 6:244–247
De Cock KM et al (2000) Prevention of mother-to-child HIV transmission in resource-poor countries. J Am Med Assoc 283:1175–1182
Woo D, Cummins M, Davies PA, Harvey DR, Hurley R, Waterson AP (1979) Vertical transmission of hepatitis B surface antigen in carrier mothers in two west London hospitals. Arch Dis Child 54:670–675
Favre M, Majewski S, De Jesus N, Malejczyk M, Orth G, Jablonska S (1998) A possible vertical transmission of human papillomavirus genotypes associated with epidermodysplasia verruciformis. J Invest Dermatol 111:333–336
McCallum H, Barlow N, Hone J (2001) How should pathogen transmission be modelled? Trends Ecol Evol 16:295–300
Lipsitch M, Siller S, Nowak MA (1996) The evolution of virulence in pathogens with vertical and horizontal transmission. Evolution 50:1729–1741
Bull JJ, Molineux I, Rice WR (1991) Selection of benevolence in a host–parasite system. Evolution 45:875–882
Ewald PW (1987) Transmission modes and evolution of the parasitism–mutualism continuum. Ann NY Acad Sci 503:295–306
De Jong MCM, Diekmann O, Heesterbeek JAP (1994) How does infection transmission depend on population size? In: Mollison D (ed) Epidemic models, their structure and relation in data. Cambridge University Press, Cambridge
Acknowledgments
Research is supported by the Department of Mathematics, Jadavpur University, PURSE DST, Government of India.
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Roy, P.K., Mondal, J., Chatterjee, S. (2011). Vertical Incidence Increases Virulence in Pathogens: A Model Based Study. In: Ao, SI., Gelman, L. (eds) Electrical Engineering and Applied Computing. Lecture Notes in Electrical Engineering, vol 90. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1192-1_52
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DOI: https://doi.org/10.1007/978-94-007-1192-1_52
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