Modelling the Periodic Outbreak of Measles in Mainland China

Abstract

In mainland China, measles infection reached the lowest level in 2012 but resurged again after that with a seasonally fluctuating pattern. To investigate the phenomenon of periodic outbreak and identify the crucial parameters that play in the transmission dynamics of measles, we formulate a mathematical model incorporating periodic transmission rate and asymptomatic infection with waning immunity. We define the basic reproduction number as the threshold value to govern whether measles infection dies out or not. Fitting the reported measles cases from 2013 to 2016 to our proposed model, we estimate the basic reproduction number R0 with immunization to be 1.0077. From numerical simulations, we conclude asymptomatic infection does not cause much new infections and the key parameters affecting the transmission of measles are vaccination rate, transmission rate, and recovery rate, which suggests the public to enhance vaccination and protection measures to reduce effective contacts between susceptible and infective individuals and treat infected individuals timely. To minimize the number of infected individuals at a minimal cost, we formulate an optimal control system to design optimal control strategies. Numerical simulations show the effectiveness of optimal control strategies and recommend us to implement the control strategies as soon as possible. In particular, enhancing vaccination is especially effective in lowering the initial outbreak and making disease recurrence less likely.

Stability and Threshold Dynamics in a Seasonal Mathematical Model for Measles Outbreaks with Double-Dose Vaccination

“…To show how well model (1) with periodic parameters matches seasonal fluctuation data, the simulation results are shown. Here, following [19,20,35,36], we assume that the transmission rate β(t) is a timeperiodic function with 12 months as a period, given by…”

“…The parameters were estimated from demographic and epidemiological data, and numerical simulations showed the seasonal fluctuation of measles in China. Xue et al [19] used the model to investigate the periodic outbreak in mainland China; they recommended enhancing vaccination and implementing an optimal control system to minimize infections. The authors of [20] analyzed the seasonal spread of measles in China using a mathematical model that accounted for periodic transmission fluctuations.…”

Impact of Vaccine Failure on the Transmission Dynamics of Measles in Nigeria

“…Also, Memon et al (2020) reported that high vaccine coverage rate is vital for disease control [17]. Again, the study in [37] analyzed a dynamic model incorporating both periodic transmission and asymptomatic infection with waning immunity with the aim of identifying parameters that influence seasonal fluctuation of measles as well as provide optimal control measures to minimize the number of infected individuals and costs.…”

An infectious disease model with asymptomatic transmission and waning immunity

“…Althouse and Scarpino [2] explored the role of asymptomatic carriers in the resurgence of pertussis (whooping cough), highlighting that even if a high proportion of individuals are vaccinated, asymptomatic transmission can still sustain the disease in the population. Models have also been used to study the roles of asymptomatic transmission for other diseases, such as Zika infection [31], measles [32,46], respiratory syncytial virus (RSV) [35,42], etc.…”