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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 the ratio of the rate of the infected mosquito per human index k for λ from the first scenario.
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fig8: The ratio of ℛ0MF/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of the ratio of the rate of the infected mosquito per human index k for λ from the first scenario.

Mentions: We used real dengue epidemic data from a dengue epidemic, between the dates Nov. 25, 2008, and 2012 from SB Hospital. This includes the estimation of the basic reproductive ratio at the beginning of t.o.p. of dengue infection by using ℛ0F, ℛ0MF, and ℛ0A for ℛ0 estimation. ℛ0 magnitude estimation under the same assumption was conducted in [12], resulting in ℛ0F. We propose ℛ0MF and ℛ0A for comparing with ℛ0F for ℛ0 estimation from dengue incidence data from SB Hospital. As a results, we get ℛ0MF > 1.59 from the first scenario (Table 4, Figures 7 and 9) and ℛ0MF > 1.40 from the second scenario, respectively (Table 6, Figures 7 and 9). From the first scenario, we obtained the the basic reproductive ratio was lowest in the t.o.p. II [1.01,2.33) and largest in the t.o.p. III [3.10,9.13) (Table 10, Figures 8 and 10). Furthermore, from the second scenario, the basic reproductive ratio was lowest in the t.o.p. II [2 .37,7.93) and largest in the t.o.p. III [5.48,11.78) (Table 11, Figures 8 and 10). We believe that ℛ0MF and ℛ0A are a good ℛ0 estimation at the beginning of the take-off period of infection. Thus, our results can be considered in the control of a dengue fever epidemic, in the dengue endemic regions of Bandung, Indonesia. But the effects of dengue incidence data were obtained from SB Hospital, Bandung, to the value of ℛ0 estimation, and describe the transmission of dengue fever, because only the dengue incidence data of the same serotype were considered.


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 the ratio of the rate of the infected mosquito per human index k for λ from the first scenario.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig8: The ratio of ℛ0MF/ℛ0F for the dengue outbreak at the beginning of the t.o.p. as a function of the ratio of the rate of the infected mosquito per human index k for λ from the first scenario.
Mentions: We used real dengue epidemic data from a dengue epidemic, between the dates Nov. 25, 2008, and 2012 from SB Hospital. This includes the estimation of the basic reproductive ratio at the beginning of t.o.p. of dengue infection by using ℛ0F, ℛ0MF, and ℛ0A for ℛ0 estimation. ℛ0 magnitude estimation under the same assumption was conducted in [12], resulting in ℛ0F. We propose ℛ0MF and ℛ0A for comparing with ℛ0F for ℛ0 estimation from dengue incidence data from SB Hospital. As a results, we get ℛ0MF > 1.59 from the first scenario (Table 4, Figures 7 and 9) and ℛ0MF > 1.40 from the second scenario, respectively (Table 6, Figures 7 and 9). From the first scenario, we obtained the the basic reproductive ratio was lowest in the t.o.p. II [1.01,2.33) and largest in the t.o.p. III [3.10,9.13) (Table 10, Figures 8 and 10). Furthermore, from the second scenario, the basic reproductive ratio was lowest in the t.o.p. II [2 .37,7.93) and largest in the t.o.p. III [5.48,11.78) (Table 11, Figures 8 and 10). We believe that ℛ0MF and ℛ0A are a good ℛ0 estimation at the beginning of the take-off period of infection. Thus, our results can be considered in the control of a dengue fever epidemic, in the dengue endemic regions of Bandung, Indonesia. But the effects of dengue incidence data were obtained from SB Hospital, Bandung, to the value of ℛ0 estimation, and describe the transmission of dengue fever, because only the dengue incidence data of the same serotype were considered.

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