Background Group A streptococcus (GAS) is the most frequent cause of bacterial pharyngitis in school-aged children. The postinfection sequel as acute rheumatic fever (ARF) and rheumatic heart disease that cause morbidity and mortality among young people is public health concerns in several developing countries. Asymptomatic carriage state of GAS is not fully understood in terms of host and bacterial factors. Although the ability of transmitting GAS of the asymptomatic carriers is relatively low, they may present the reservoir of the epidemic. A fraction of GAS carriers is difficult to estimate in practice and may greatly vary between populations. Understanding the role of carriage on the transmission dynamic of GAS is important for assessing the public health impact of the ARF. Method This study investigates the effect of GAS carriers on both the transmission and dynamic of ARF cases by using a mathematical model. Result We derive the sufficient conditions for which the GAS can spread or extinct from the naive population under the variation of the fraction of symptomatic cases over the incidence of GAS. The threshold is possible to occur in general, but the last condition which is rather restrictive and involves parameter uncertainty. The increasing of carriers in the endemic state leads to the reduction in magnitude of the reproduction number and the number of ARF patients. We demonstrate that the adjustment of parameters can be carried out by the use of endemic state and some specific data. Conclusion We show theoretically that the presence of asymptomatic carriers may induce the epidemic threshold and reduce the virulence of GAS and the prevalence of ARF.

Quantifying the effects of control measures during the emergence and recurrence of SARS-CoV-2 poses a challenge to understanding the dynamic responses in terms of effectiveness and the population’s reaction. This study aims to estimate and compare the non-pharmaceutical interventions applied in the first and second outbreaks of COVID-19 in Thailand. We formulated a dynamic model of transmission and control. For each outbreak, the time interval was divided into subintervals characterized by epidemic events. We used daily case report data to estimate the transmission rates, the quarantine rate, and its efficiency by the maximum likelihood method. The duration-specific control reproduction numbers were calculated. The model predicts that the reproduction number dropped by about 91% after the nationwide lockdown in the first wave. In the second wave, after a high number of cases had been reported, the reproduction number decreased to about 80% in the next phase, but the spread continued. The estimated value was below the threshold in the last phase. For both waves, successful control was mainly induced by decreased transmission rate, while the explicit quarantine measure showed less effectiveness. The relatively weak control measure estimated by the model may have implications for economic impact and the adaptation of people.

Antibiotic treatment failure related to carriers poses a serious problem to physicians and epidemiologists. Due to the sparsity of data, assessing the role in infection dynamics is difficult. In this study, we examined the possibility that a particular therapeutic effectiveness will be regarded as the disease extinction threshold through the mathematical modelling approach. Including the treatment state in the generic epidemic model with carrier allows us to describe the role of carriers in the treatment failure. The parameterized extinction thresholds were derived via the basic reproduction number for deterministic model, and via the Jury stability criterion for the stochastic model. Existence conditions for the stochastic threshold were derived without the exact formula of the spectral radius of the expectation matrix. The results show that the transmissibility of carrier is necessary for the extinction threshold via treatment failure. The expected extinction threshold may occur subject to the certain range of the transmission potential of the symptomatic infection. This existence conditions are independent of the rate at which the carriers undergo treatment and can be used to support a control strategy.

Identifying the relationship between human mobility, air pollution, and communicable disease poses a challenge for impact evaluation and public health planning. Specifically, Coronavirus disease 2019 (COVID-19) and air pollution from fine particulates (PM2.5), by which human mobility is mediated in a public health emergency. To describe the interplay between human mobility and PM2.5 during the spread of COVID-19, we proposed a nonlinear model of the time-dependent transmission rate as a function of these factors. A compartmental epidemic model, together with daily confirmed case data in Bangkok, Thailand during 2020–2021, was used to estimate the intrinsic parameters that can determine the impact on the transmission dynamic of the two earlier outbreaks. The results suggested a positive association between mobility and transmission, but this was strongly dependent on the context and the temporal characteristics of the data. For the ascending phase of an epidemic, the estimated coefficient of mobility variable in the second wave was greater than in the first wave, but the value of the mobility component in the transmission rate was smaller. Due to the influence of the baseline value and PM2.5, the estimated basic reproduction number of the second wave was higher than that of the first wave, even though mobility had a greater influence. For the descending phase, the value of the mobility component in the second wave was greater, due to the negative value of the estimated mobility coefficient. Despite this scaling effect, the results suggest a negative association between PM2.5 and the transmission rates. Although this conclusion agrees with some previous studies, the true effect of PM2.5 remains inconclusive and requires further investigation.