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,？Rc？(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 (ΛM) 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 Rc？＜ 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.
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
Reiter, P. (2007) Oviposition, Dispersed and Survival in Aedes aegypti: Implication for the Efficiency of Control Strategies. Vector-Borne Zoonetic Disease, 7, 261-273.
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
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
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.
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.
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.
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.
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.