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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

PRCC values for chikungunya models (10) and (32), using as response functions (a) the reproduction number ℛ0; (b) the reproduction number ℛH. Parameter values (baseline) and ranges used are as given in Table 3.
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fig6: PRCC values for chikungunya models (10) and (32), using as response functions (a) the reproduction number ℛ0; (b) the reproduction number ℛH. Parameter values (baseline) and ranges used are as given in Table 3.

Mentions: Sensitivity analysis [60–62] is carried out, on the parameters of the age-structured chikungunya model (10), to determine which of the parameters have the most significant impact on the outcome of the numerical simulations of the model. Figure 6(a) depicts the partial rank correlation coefficient (PRCC) values for each parameter of the models, using the ranges and baseline values tabulated in Table 3 (with the basic reproduction number, ℛ0, as the response function), from which it follows that the parameters that have the most influence on chikungunya transmission dynamics are the mosquito biting rate (bM), the transmission probability per contact in mosquitoes (βM) and in humans (βS), mosquito recruitment rate (πM), and the death rate of the mosquitoes (μM). It is interesting to note that, from Figure 6(a), the transmission probability per contact in juvenile and adult (βJ and βA) is not as significant as that of the seniors. Thus, this study identifies the most important parameters that drive the transmission mechanism of the disease. The identification of these key parameters is vital to the formulation of effective control strategies for combating the spread of the disease. In other words, the results of this sensitivity analysis suggest that a strategy that reduces the mosquito biting rate (reduces bM), the mosquito recruitment rate (reduces πM), and the transmission probability per contact in mosquitoes (reduces βM) and in humans (reduces βS) and increases the death rate of the mosquito (increases μM) will be effective in curtailing the spread of chikungunya virus in the community.


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

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

PRCC values for chikungunya models (10) and (32), using as response functions (a) the reproduction number ℛ0; (b) the reproduction number ℛH. Parameter values (baseline) and ranges used are as given in Table 3.
© Copyright Policy
Related In: Results  -  Collection

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

fig6: PRCC values for chikungunya models (10) and (32), using as response functions (a) the reproduction number ℛ0; (b) the reproduction number ℛH. Parameter values (baseline) and ranges used are as given in Table 3.
Mentions: Sensitivity analysis [60–62] is carried out, on the parameters of the age-structured chikungunya model (10), to determine which of the parameters have the most significant impact on the outcome of the numerical simulations of the model. Figure 6(a) depicts the partial rank correlation coefficient (PRCC) values for each parameter of the models, using the ranges and baseline values tabulated in Table 3 (with the basic reproduction number, ℛ0, as the response function), from which it follows that the parameters that have the most influence on chikungunya transmission dynamics are the mosquito biting rate (bM), the transmission probability per contact in mosquitoes (βM) and in humans (βS), mosquito recruitment rate (πM), and the death rate of the mosquitoes (μM). It is interesting to note that, from Figure 6(a), the transmission probability per contact in juvenile and adult (βJ and βA) is not as significant as that of the seniors. Thus, this study identifies the most important parameters that drive the transmission mechanism of the disease. The identification of these key parameters is vital to the formulation of effective control strategies for combating the spread of the disease. In other words, the results of this sensitivity analysis suggest that a strategy that reduces the mosquito biting rate (reduces bM), the mosquito recruitment rate (reduces πM), and the transmission probability per contact in mosquitoes (reduces βM) and in humans (reduces βS) and increases the death rate of the mosquito (increases μM) will be effective in curtailing the spread of chikungunya virus in the community.

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