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

Agusto FB, Easley S, Freeman K, Thomas M - Comput Math Methods Med (2016)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, USA.

ABSTRACT
We developed a new age-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.

No MeSH data available.


Related in: MedlinePlus

Backward bifurcation plot for without age-structured model (32). (a) Asymptomatic humans; (b) symptomatic humans. Parameter values used are as given in Table 3.
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fig5: Backward bifurcation plot for without age-structured model (32). (a) Asymptomatic humans; (b) symptomatic humans. Parameter values used are as given in Table 3.

Mentions: However, if δAH, δSH ≠ 0, then it follows that the reduced model (32) will undergo backward bifurcation if the coefficient a, in this case, given as(37)a=−2bMv2w8x1w2+w3+w5βH+v7w3x6w3+w1+w2+w5βM−v7w3w6x1βMx12,is positive, where(38)w1=−βHbMw8g1μM,w2=βHbMw8g2,w3=εHσHw2g3,w4=1−εHσHw2g4,w5=γAHw3+γSHw4g5,w6=−x6βMbMw3+w4μMx1,w7=x6βMbMw3+w4g6x1,w8>0,v1=0,v5=0,v6=0,v2=εHσHv3+1−εHσHv4g2,v3=1g3γAHv5+x6βMbMv7−v6x1,v4=1g4γSHv5+x6βMbMv7−v6x1,v7=σMv8g6,v8=βHbMv2μMwith g1 = μH, g2 = σH + μH, g3 = γAH + μH + δAH, g4 = γSH + μH + δSH, g5 = μH, and (39)b=v7x6bMw3x1>0.The phenomenon of backward bifurcation for model (32) without age structure is illustrated numerically in Figure 5.


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

Agusto FB, Easley S, Freeman K, Thomas M - Comput Math Methods Med (2016)

Backward bifurcation plot for without age-structured model (32). (a) Asymptomatic humans; (b) symptomatic humans. Parameter values used are as given in Table 3.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4835678&req=5

fig5: Backward bifurcation plot for without age-structured model (32). (a) Asymptomatic humans; (b) symptomatic humans. Parameter values used are as given in Table 3.
Mentions: However, if δAH, δSH ≠ 0, then it follows that the reduced model (32) will undergo backward bifurcation if the coefficient a, in this case, given as(37)a=−2bMv2w8x1w2+w3+w5βH+v7w3x6w3+w1+w2+w5βM−v7w3w6x1βMx12,is positive, where(38)w1=−βHbMw8g1μM,w2=βHbMw8g2,w3=εHσHw2g3,w4=1−εHσHw2g4,w5=γAHw3+γSHw4g5,w6=−x6βMbMw3+w4μMx1,w7=x6βMbMw3+w4g6x1,w8>0,v1=0,v5=0,v6=0,v2=εHσHv3+1−εHσHv4g2,v3=1g3γAHv5+x6βMbMv7−v6x1,v4=1g4γSHv5+x6βMbMv7−v6x1,v7=σMv8g6,v8=βHbMv2μMwith g1 = μH, g2 = σH + μH, g3 = γAH + μH + δAH, g4 = γSH + μH + δSH, g5 = μH, and (39)b=v7x6bMw3x1>0.The phenomenon of backward bifurcation for model (32) without age structure is illustrated numerically in Figure 5.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, USA.

ABSTRACT
We developed a new age-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.

No MeSH data available.


Related in: MedlinePlus