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Estimation of the Basic Reproductive Ratio for Dengue Fever at the Take-Off Period of Dengue Infection.

- Comput Math Methods Med (2015)

Bottom Line: The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans.Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa.We conclude that the second approach is more realistic, compared with our first approach and the previous work.

View Article: PubMed Central - PubMed

Affiliation: Departemen Matematika, FMIPA, Institut Teknologi Bandung, Bandung, Indonesia ; Jurusan Matematika, FST, Universitas Nusa Cendana, Kupang, Indonesia.

ABSTRACT
Estimating the basic reproductive ratio ℛ 0 of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paper we propose two different constructions to estimate ℛ 0 which is derived from a dynamical system of host-vector dengue transmission model. The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infected mosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in which the dynamics of an infected human compartments are intervened by the dynamics of an infected mosquito compartment, and vice versa. We apply our construction to the real dengue epidemic data from SB Hospital, Bandung, Indonesia, during the period of outbreak Nov. 25, 2008-Dec. 2012. We also propose two scenarios to determine the take-off rate of infection at the beginning of a dengue epidemic for construction of the estimates of ℛ 0: scenario I from equation of new cases of dengue with respect to time (daily) and scenario II from equation of new cases of dengue with respect to cumulative number of new cases of dengue. The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans. Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa. We conclude that the second approach is more realistic, compared with our first approach and the previous work.

No MeSH data available.


Related in: MedlinePlus

The ratio of ℛ0MF/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of ratio of the rate of the infected mosquito per human index k for λ from the second scenario.
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fig12: The ratio of ℛ0MF/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of ratio of the rate of the infected mosquito per human index k for λ from the second scenario.

Mentions: In the first scenario, the control of dengue fever, which is based on the standard value ℛ0F, is still realistic. Furthermore, better control of dengue fever, when based on the maximum value of ℛ0MF or maximum value of ℛ0A, is shown in Table 6 and Figures 7–10. While for the second scenario, which is shown by Table 6 and Figures 11–14, it is better to choose one value from the interval as a standard value used to control dengue fever. Therefore, the second construction is better choice, for dengue control strategies in Bandung, Indonesia. Nevertheless, the estimation of ℛ0 has limitations, because it is only done from the fourth day until the seventh day, so the effect of the increase in the incidence of dengue ℛ0 is no longer considered. Furthermore, the dengue incidence data used, from SB Hospital, do not distinguish between the latent population and the dengue infected human population, so the estimate of ℛ0 is limited by the data characteristics. In reality, nobody can distinguish between the latent population and the dengue infected population. Furthermore the latent population has a short incubation time period.


Estimation of the Basic Reproductive Ratio for Dengue Fever at the Take-Off Period of Dengue Infection.

- Comput Math Methods Med (2015)

The ratio of ℛ0MF/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of ratio of the rate of the infected mosquito per human index k for λ from the second scenario.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4561940&req=5

fig12: The ratio of ℛ0MF/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of ratio of the rate of the infected mosquito per human index k for λ from the second scenario.
Mentions: In the first scenario, the control of dengue fever, which is based on the standard value ℛ0F, is still realistic. Furthermore, better control of dengue fever, when based on the maximum value of ℛ0MF or maximum value of ℛ0A, is shown in Table 6 and Figures 7–10. While for the second scenario, which is shown by Table 6 and Figures 11–14, it is better to choose one value from the interval as a standard value used to control dengue fever. Therefore, the second construction is better choice, for dengue control strategies in Bandung, Indonesia. Nevertheless, the estimation of ℛ0 has limitations, because it is only done from the fourth day until the seventh day, so the effect of the increase in the incidence of dengue ℛ0 is no longer considered. Furthermore, the dengue incidence data used, from SB Hospital, do not distinguish between the latent population and the dengue infected human population, so the estimate of ℛ0 is limited by the data characteristics. In reality, nobody can distinguish between the latent population and the dengue infected population. Furthermore the latent population has a short incubation time period.

Bottom Line: The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans.Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa.We conclude that the second approach is more realistic, compared with our first approach and the previous work.

View Article: PubMed Central - PubMed

Affiliation: Departemen Matematika, FMIPA, Institut Teknologi Bandung, Bandung, Indonesia ; Jurusan Matematika, FST, Universitas Nusa Cendana, Kupang, Indonesia.

ABSTRACT
Estimating the basic reproductive ratio ℛ 0 of dengue fever has continued to be an ever-increasing challenge among epidemiologists. In this paper we propose two different constructions to estimate ℛ 0 which is derived from a dynamical system of host-vector dengue transmission model. The construction is based on the original assumption that in the early states of an epidemic the infected human compartment increases exponentially at the same rate as the infected mosquito compartment (previous work). In the first proposed construction, we modify previous works by assuming that the rates of infection for mosquito and human compartments might be different. In the second construction, we add an improvement by including more realistic conditions in which the dynamics of an infected human compartments are intervened by the dynamics of an infected mosquito compartment, and vice versa. We apply our construction to the real dengue epidemic data from SB Hospital, Bandung, Indonesia, during the period of outbreak Nov. 25, 2008-Dec. 2012. We also propose two scenarios to determine the take-off rate of infection at the beginning of a dengue epidemic for construction of the estimates of ℛ 0: scenario I from equation of new cases of dengue with respect to time (daily) and scenario II from equation of new cases of dengue with respect to cumulative number of new cases of dengue. The results show that our first construction of ℛ 0 accommodates the take-off rate differences between mosquitoes and humans. Our second construction of the ℛ 0 estimation takes into account the presence of infective mosquitoes in the early growth rate of infective humans and vice versa. We conclude that the second approach is more realistic, compared with our first approach and the previous work.

No MeSH data available.


Related in: MedlinePlus