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

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.

On the Analysis of Covid-19 Transmission in Wuhan, Diamond Princess and Jakarta-cluster

“…Here we construct the basic reproductive ratio using the take-off rate at the early infection [11], [12] by assuming that the incidences as well as the cumulative incidence K(t) grow with a take-off rate θ during the take-off period:…”

“…By differentiating (12) and with the use of ( 10) we have the following equation The time t = τ is achieved when contact tracing and isolation are completed, i.e. there is no more new infection from the contact with infected persons.…”

Estimasi Bilangan Reproduksi Dasar Penyebaran Penyakit Demam Berdarah Dengue Di Kota Bima Tahun 2018 - 2020

“…Model matematika yang digunakan adalah model standar host-vector penyebaran demam berdarah yang sudah ada pada berbagai literature. Model standar itu kami gunakan sebagaimana pada referensi [11]. Keaslian dari naskah ini adalah perhitungan angka reproduksi dasar.…”

Prediction of the peak Covid-19 pandemic in Indonesia using SIR model

“…Tingkat reproduksi relatif terhadap waktu Ro(t) dapat diadaptasi dari persamaan tersebut dan dapat dihitung dengan Persamaan 5. 6) Jika diberikan informasi aktual mengenai data susceptible, infected, dan removed dalam periode waktu [0, T] maka tingkat reproduksi efektif R 0 := 1…”