Limits...
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

Level set for ℛ0MF2/ℛ0F2 in (15) for data set {μv = 1/30, λ ∈ [0,0.20], k ∈ [0,20]}.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4561940&req=5

fig2: Level set for ℛ0MF2/ℛ0F2 in (15) for data set {μv = 1/30, λ ∈ [0,0.20], k ∈ [0,20]}.

Mentions: Next we introduce our construction of ℛ0 estimation. The first construction is derived under the assumption that, at the beginning of dengue infection, the take-off rate of the host and vector varies differently; that is (12)Iht≈Ih0eλt,Ivt≈Iv0ekλt,where k > 0 is the rate of infected mosquitoes per human index. Using the same process as in the derivation of ℛ0F, one obtains (13)R0MF2λμh+γ+1kλμv+1=b2phpvμvμh+γNvNh=R02or, equivalently, (14)R0MF=kλ2μvμh+γ+μv+kμh+γλμvμh+γ+1.Note that ℛ0F is a special case from ℛ0MF; that is, if k = 1 then ℛ0F = ℛ0MF. In reality ℛ0MF is more realistic than ℛ0F. From (11) and (14) we obtain(15)R0MF2R0F2=1+k−1λλ+μv.The comparison between ℛ0MF and ℛ0F is shown as the level set of (15) in Figure 2.


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

- Comput Math Methods Med (2015)

Level set for ℛ0MF2/ℛ0F2 in (15) for data set {μv = 1/30, λ ∈ [0,0.20], k ∈ [0,20]}.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig2: Level set for ℛ0MF2/ℛ0F2 in (15) for data set {μv = 1/30, λ ∈ [0,0.20], k ∈ [0,20]}.
Mentions: Next we introduce our construction of ℛ0 estimation. The first construction is derived under the assumption that, at the beginning of dengue infection, the take-off rate of the host and vector varies differently; that is (12)Iht≈Ih0eλt,Ivt≈Iv0ekλt,where k > 0 is the rate of infected mosquitoes per human index. Using the same process as in the derivation of ℛ0F, one obtains (13)R0MF2λμh+γ+1kλμv+1=b2phpvμvμh+γNvNh=R02or, equivalently, (14)R0MF=kλ2μvμh+γ+μv+kμh+γλμvμh+γ+1.Note that ℛ0F is a special case from ℛ0MF; that is, if k = 1 then ℛ0F = ℛ0MF. In reality ℛ0MF is more realistic than ℛ0F. From (11) and (14) we obtain(15)R0MF2R0F2=1+k−1λλ+μv.The comparison between ℛ0MF and ℛ0F is shown as the level set of (15) in Figure 2.

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