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Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus


Affiliations
1 Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, United States
2 Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, United States
 

We developed a newage-structured deterministic model for the transmission dynamics of chikungunya virus. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the stable disease-free equilibrium is globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model undergoes, in the presence of disease induced mortality, the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the qualitative dynamics of the model are not altered by the inclusion of age structure. This is further emphasized by the sensitivity analysis results, which shows that the dominant parameters of the model are not altered by the inclusion of age structure. However, the numerical simulations show the flaw of the exclusion of age in the transmission dynamics of chikungunya with regard to control implementations.The exclusion of age structure fails to show the age distribution needed for an effective age based control strategy, leading to a one size fits all blanket control for the entire population.
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  • Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus

Abstract Views: 104  |  PDF Views: 1

Authors

Folashade B. Agusto
Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, United States
Shamise Easley
Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, United States
Kenneth Freeman
Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, United States
Madison Thomas
Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, United States

Abstract


We developed a newage-structured deterministic model for the transmission dynamics of chikungunya virus. The model is analyzed to gain insights into the qualitative features of its associated equilibria. Some of the theoretical and epidemiological findings indicate that the stable disease-free equilibrium is globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model undergoes, in the presence of disease induced mortality, the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. Further analysis of the model indicates that the qualitative dynamics of the model are not altered by the inclusion of age structure. This is further emphasized by the sensitivity analysis results, which shows that the dominant parameters of the model are not altered by the inclusion of age structure. However, the numerical simulations show the flaw of the exclusion of age in the transmission dynamics of chikungunya with regard to control implementations.The exclusion of age structure fails to show the age distribution needed for an effective age based control strategy, leading to a one size fits all blanket control for the entire population.