Investigation of a measles transmission with vaccination: a case study in Jakarta, Indonesia

1.
Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
2.
Jakarta Provincial Health Office, Jakarta 10160, Indonesia

Received: 26 December 2019 Accepted: 22 March 2020 Published: 01 April 2020

Abstract
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Measles is a contagious disease caused by the measles virus of genus Morbillivirus, which has been spreading in many affected regions. This infection is characterized by the appearance of rashes all over the body and potentially cause serious complications, especially among infants and children. Before measles immunization was promoted, it is one of the endemic diseases that caused the most fatalities each year in the world. This paper aims to analyze and to investigate measles transmission in Jakarta via an SIHR epidemic model involving vaccination from January to December 2017. Jakarta Health Office collected the observed data of measles incidence. We then derived the basic reproduction number as a threshold of disease transmission and obtained the local as well as global stability of the equilibria under certain conditions. The unobserved parameters and initial conditions were estimated by minimizing errors between data and numerical results. Furthermore, a stochastic model was developed to capture the data and to accommodate the randomness of the transmission. Sensitivity analysis was also performed to analyze and to identify the parameters which give significant contributions to the spread of the virus. We then obtained simulations of vaccine level coverage. The data is shown within a 95% confidence interval of the stochastic solutions, and the average of the stochastic solutions is relatively close to the solution of the deterministic model. The most sensitive parameter in the infected compartment is the hospitalized rate, which can be considered to be one of the essential factors to reduce the number of cases for policymakers. We hence proposed a control strategy which is providing treatment accesses easier for infected individuals is better than vaccinating when an outbreak occurs.
- measles,
- stability,
- parameter estimation,
- sensitivity analysis,
- control strategy
Citation: Muhammad Fakhruddin, Dani Suandi, Sumiati, Hilda Fahlena, Nuning Nuraini, Edy Soewono. Investigation of a measles transmission with vaccination: a case study in Jakarta, Indonesia[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 2998-3018. doi: 10.3934/mbe.2020170

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Abstract

Measles is a contagious disease caused by the measles virus of genus Morbillivirus, which has been spreading in many affected regions. This infection is characterized by the appearance of rashes all over the body and potentially cause serious complications, especially among infants and children. Before measles immunization was promoted, it is one of the endemic diseases that caused the most fatalities each year in the world. This paper aims to analyze and to investigate measles transmission in Jakarta via an SIHR epidemic model involving vaccination from January to December 2017. Jakarta Health Office collected the observed data of measles incidence. We then derived the basic reproduction number as a threshold of disease transmission and obtained the local as well as global stability of the equilibria under certain conditions. The unobserved parameters and initial conditions were estimated by minimizing errors between data and numerical results. Furthermore, a stochastic model was developed to capture the data and to accommodate the randomness of the transmission. Sensitivity analysis was also performed to analyze and to identify the parameters which give significant contributions to the spread of the virus. We then obtained simulations of vaccine level coverage. The data is shown within a 95% confidence interval of the stochastic solutions, and the average of the stochastic solutions is relatively close to the solution of the deterministic model. The most sensitive parameter in the infected compartment is the hospitalized rate, which can be considered to be one of the essential factors to reduce the number of cases for policymakers. We hence proposed a control strategy which is providing treatment accesses easier for infected individuals is better than vaccinating when an outbreak occurs.

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