Modelling the Effects of Vertical Transmission in Mosquito and the Use of Imperfect Vaccine on Chikungunya Virus Transmission Dynamics — Oak Academic Publishing
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Modelling the Effects of Vertical Transmission in Mosquito and the Use of Imperfect Vaccine on Chikungunya Virus Transmission Dynamics
Department of Physical Sciences, Kampala International University, Kampala, Uganda
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Department of Science Laboratory Technology, Federal Polytechnic Nasarawa, Nasarawa, Nigeria
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Department of Mathematics and Statistics, Islamic University in Uganda, Mbale, Uganda
1 Department of Physical Sciences, Kampala International University, Kampala, Uganda
2 Department of Science Laboratory Technology, Federal Polytechnic Nasarawa, Nasarawa, Nigeria
3 Department of Mathematics and Statistics, Islamic University in Uganda, Mbale, Uganda
In this paper, a deterministic mathematical model for Chikungunya virus (Chikv) transmission and control is developed and analyzed to underscore the effect of vaccinating a proportion of the susceptible human, and vertical transmission in mosquito population. The disease free, and endemic equilibrium states were obtained and the conditions for the local and global stability or otherwise were given. Sensitivity analysis of the effective reproductive number, R c (the number of secondary infections resulting from the introduction of a single infected individual into a population where a proportion is fairly protected) shows that the recruitment rate of susceptible mosquito ( Λ M ) and the proportion of infectious new births from infected mosquito ( β ) are the most sensitive parameters. Bifurcation analysis of the model using center manifold theory reveals that the model undergoes backward bifurcation (coexistence of disease free and endemic equilibrium when R c ＜ 1 ) . Numerical simulation of the model shows that vaccination of susceptible human population with imperfect vaccine will have a positive impact and that vertical transmission in mosquito population has a negligible effect. To the best of our knowledge, our model is the first to incorporate vaccinated human compartment and vertical transmission in (Chikv) model.
Robinson, M.C. (1955) An Epidemic of Virus Disease in Southern Province, Tanganyika Territory, in 1952-1953. I. Clinical Features. Transactions of the Royal Society of Tropical Medicine and Hygiene, 49, 28-32. https://doi.org/10.1016/0035-9203(55)90080-8
Vazeille, M., Moutailler, S., Coudrier, D., Rousseaux, C., Khun, H., et al. (2007) Two Chikungunya Isolates from the Outbreak of La Reunion (Indian Ocean) Exhibit Different Patterns of Infection in the Mosquito, Aedes albopictus. PLoS ONE, 2, e1168. https://doi.org/10.1371/journal.pone.0001168
Moore, D.L., Readdy, S., Akinkugbe, F.M., Lee, V.H., David-West, T.S., Causey, O.R. and Carez, D.E. (1974) An Epidemic of Chikungunya Fever at Ibadan, Nigeria, 1969. Annals of Tropical Medicine & Parasitology, 68, 59-68. https://doi.org/10.1080/00034983.1974.11686925
World Health Organisation (2017). http://www.who.int/mediacentre/factsheets/fs327/en/
Chandrakant, L., and Pradhan, S.K. (2006) Emergence of Chikungunya Virus in India Subcontinent after 32 Years, a Review. Journal of Vector Borne Diseases, 43, 151-160.
Pialoux, G., Gauze‘re, B.A., Jaureguiberry, S. and Strobel, M. (2007) Chikungunya, an Epidemic Arbovirosis. The Lancet, 7, 319-327. https://doi.org/10.1016/S1473-3099(07)70107-X
Peterson, L. R., and Powers, A.M. (2016) Chikungunya: Epidemiology. F1000 Research, 5, 82-89.
Reiter, P. (2007) Oviposition, Dispersed and Survival in Aedes aegypti: Implication for the Efficiency of Control Strategies. Vector-Borne Zoonetic Disease, 7, 261-273. https://doi.org/10.1089/vbz.2006.0630
Bonizzoni, M., Gezperi, G., Chen, X. and James, A.A. (2013) The Invasive Mosquito Species Aedes albopictus: Current Knowledge and Future Perspective. Trends in Parasitology, 29, 460-468. https://doi.org/10.1016/j.pt.2013.07.003
Rao, G., Khan, Y.Z. and Chitnis D.S. (2008) Chikungunya Infection in Neonates. Indian Pediatics, 45, 240-244.
Anderson, R.M. and May, R.M. (1991) Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford.
Hethcote, H.W. (2000) The Mathematics of Infectious Diseases. SIAM Review, 42, 599-653. https://doi.org/10.1137/S0036144500371907
Diekman, O. and Heesterbeck, J.A.P. (2000) Mathematical Epidemiology of Infectious Diseases. Wiley-Blackwell, New York.
Dumont, Y., Chiroleu, F. and Domerg, C. (2008) On a Temporal Model for the Chikungunya Disease: Modeling, Theory and Numerics. Mathematical Biosciences, 213, 80-91. https://doi.org/10.1016/j.mbs.2008.02.008
Moulay, D., Aziz-Alaoui, M.A. and Cadivel, M. (2011) The Chikungunya Disease: Modeling, Vector and Transmission Global Dynamics. Mathematical Biosciences, 229, 50-63. https://doi.org/10.1016/j.mbs.2010.10.008
Ruiz-Moreno, D., Vargas, I.S., Olson, K.E. and Harrington, L.C. (2012) Modeling Dynamic Introduction of Chikungunya Virus in the United States. PLoS Neglected Tropical Disease, 6, e1918. https://doi.org/10.1371/journal.pntd.0001918
Pongsumpun, P. and Sangsawangl, S. (2013) Local Stability Analysis for Age Structural Model of Chikungunya Disease. Journal of Basic and Applied Scientific Research, 3, 302-312.
Yakob, L. and Clements, A.C.A. (2013) A Mathematical Model of Chikungunya Dynamics and Control: The Major Epidemic on Réunion Island. PLoS ONE, 8, e57448. https://doi.org/10.1371/journal.pone.0057448
Manore, C.A., Hickmann, K.S., Xu, S., Wearing, H.J. and Hyman, J.M. (2014) Comparing Dengue and Chikungunya Emergence and Endemic Transmission in A. aegypti and A. albopictus. Journal of Theoretical Biology, 356, 174-191. https://doi.org/10.1016/j.jtbi.2014.04.033
Chitnis, N., Hyman, J.M. and Cushing, J.M. (2008) Determining Important Parameters in the Spread of Malaria through the Sensitivity Analysis of a Mathematical Model. Bulletin of Mathematical Biology, 70, 1272-1296. https://doi.org/10.1007/s11538-008-9299-0
Dumont, Y. and Chiroleu, F. (2010) Vector Control for the Chikungunya Disease. Mathematical Biosciences and Engineering, 7, 315-348. https://doi.org/10.3934/mbe.2010.7.313
Nur Aida, H., Abu Hassan, A., Nurita, A.T., Che Salmah, M.R. and Norasmah, B. (2008) Population Analysis of Aedes albopictus (Skuse) (Diptera: Culicidae) under Uncontrolled Laboratory Conditions. Tropical Biomedicine, 25, 117-125.
Lahariya, C. and Pradhan, S.K. (2006) Emergence of Chikungunya Virus in Indian Subcontinent after 32 Years: A Review. Journal of Vector Borne Diseases, 43, 151-160.
Delatte, H., Gimonneau, G., Triboire, A. and Fontenille, D. (2009) Influence of Temperature on Immature Development, Survival, Longevity, Fecundity, and Gonotrophic Cycles of Aedes albopictus, Vector of Chikungunya and Dengue in the Indian Ocean. Journal of Medical Entomology, 46, 33-41. https://doi.org/10.1603/033.046.0105
Hethcote, H.W. (1978) An Immunization Model for a Heterogeneous Population. Theoretical Population Biology, 14, 338-349. https://doi.org/10.1016/0040-5809(78)90011-4
Institute of Epidemiology, Disease Control and Research (2017) Chikungunya News Letter. http://www.iedcr.gov.bd/index.php/chikungunya/chikungunya-newsletter
Lakshmikantham, V., Leela, S. and Martynyuk, A.A. (1989) Stability Analysis of Non-Linear Systems. Marcel Dekker, New York.
Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D. and Yakubu, A.A. (2002) Mathematical Approaches for Emerging and Reemerging Infectious Diseases. Springer-Verlag, New York.
Powell, D.R., Faie, J., Leclaire, R.J., Moore, L.M. and Thompson, D. (2005) Sensitivity Analysis of an Infectious Disease Model. International System Dynamic Conference, Boston, MA.
Castillo-Chavez, C. and Song, B. (2004) Dynamical Models of Tuberculosis and Their Applications. Mathematical Biosciences & Engineering, 1, 361-404. https://doi.org/10.3934/mbe.2004.1.361
Agosto, F.B., Easley, S., Freeman, K. and Thomas, M. (2016) Mathematical Model of Three Age Structured Transmission Dynamics of Chikungunya Virus. Computational and Mathematical Methods in Medicine, 2016, Article ID: 4320514. https://doi.org/10.1155/2016/4320514
Garba, M.S., Gumel, A.B. and Bakar, A.M.R. (2008) Backward Bifurcation in Dengue Transmission Dynamics. Mathematical Bioscience, 215, 11-25. https://doi.org/10.1016/j.mbs.2008.05.002