A mumps model with seasonality in China

A heterogeneous continuous age-structured model of mumps with vaccine

In classical mumps models, individuals are generally assumed to be uniformly mixed (homogeneous), ignoring population heterogeneity (preference, activity, etc.). Age is the key to catching mixed patterns in developing mathematical models for mumps. A continuous heterogeneous age-structured model for mumps with vaccines has been developed in this paper. The stability of age-structured models is a difficult question. An explicit formula of R 0 was defined for the various mixing modes (isolation, proportional and heterogeneous mixing) with or without the vaccine. The results show that the endemic steady state is unique and locally stable if R 0 > 1 without any additional conditions. A number of numerical examples are given to support the theory.

Exploring the seasonality and optimal control strategy of HIV/AIDS epidemic in China: The impact of seasonal testing

In this work, we investigate how the seasonal variation in the number of individuals who are tested for an HIV antibody in outpatient clinics affects the HIV transmission patterns in China, which has not been well studied. Based on the characteristics of outpatient testing data and reported cases, we establish a periodic infectious disease model to study the impact of seasonal testing on HIV transmission. The results indicate that the seasonal testing is a driving factor for the seasonality of new cases. We demonstrate the feasibility of ending the HIV/AIDS epidemic. We find that the diagnostic rates related to testing play a crucial role in controlling the size of the epidemic. Specifically, when considering minimizing both infected individuals and diagnostic rates, the level of attention paid to undiagnosed infected individuals is always positively correlated with the optimal diagnostic rates, while the optimal diagnostic rates are negatively correlated with the size of the epidemic at the terminal time.

The impact of temperature, humidity and closing school on the mumps epidemic: a case study in the mainland of China

BACKGROUND

To control resurging infectious diseases like mumps, it is necessary to resort to effective control and preventive measures. These measures include increasing vaccine coverage, providing the community with advice on how to reduce exposure, and closing schools. To justify such intervention, it is important to understand how well each of these measures helps to limit transmission.

METHODS

In this paper, we propose a simple SEILR (susceptible-exposed-symptomatically infectious-asymptomatically infectious-recovered) model by using a novel transmission rate function to incorporate temperature, humidity, and closing school factors. This new transmission rate function allows us to verify the impact of each factor either separately or combined. Using reported mumps cases from 2004 to 2018 in the mainland of China, we perform data fitting and parameter estimation to evaluate the basic reproduction number  R 0 . As a wide range of one-dose measles, mumps, and rubella (MMR) vaccine programs in China started only in 2008, we use different vaccination proportions for the first Stage I period (from 2004 to 2008) and the second Stage II period (from 2009 to 2018). This allows us to verify the importance of higher vaccine coverage with a possible second dose of MMR vaccine.

RESULTS

We find that the basic reproduction number  R 0  is generally between 1 and 3. We then use the Akaike Information Criteria to assess the extent to which each of the three factors contributed to the spread of mumps. The findings suggest that the impact of all three factors is substantial, with temperature having the most significant impact, followed by school opening and closing, and finally humidity.

CONCLUSION

We conclude that the strategy of increasing vaccine coverage, changing micro-climate (temperature and humidity), and closing schools can greatly reduce mumps transmission.

Oscillatory properties of class C notifiable infectious diseases in China from 2009 to 2021

Background

Epidemics of infectious diseases have a great negative impact on people's daily life. How it changes over time and what kind of laws it obeys are important questions that researchers are always interested in. Among the characteristics of infectious diseases, the phenomenon of recrudescence is undoubtedly of great concern. Understanding the mechanisms of the outbreak cycle of infectious diseases could be conducive for public health policies to the government.

Method

In this study, we collected time-series data for nine class C notifiable infectious diseases from 2009 to 2021 using public datasets from the National Health Commission of China. Oscillatory power of each infectious disease was captured using the method of the power spectrum analysis.

Results

We found that all the nine class C diseases have strong oscillations, which could be divided into three categories according to their oscillatory frequencies each year. Then, we calculated the oscillation power and the average number of infected cases of all nine diseases in the first 6 years (2009-2015) and the next 6 years (2015-2021) since the update of the surveillance system. The change of oscillation power is positively correlated to the change in the number of infected cases. Moreover, the diseases that break out in summer are more selective than those in winter.

Conclusion

Our results enable us to better understand the oscillation characteristics of class C infectious diseases and provide guidance and suggestions for the government's prevention and control policies.

Correlation between mumps and meteorological factors in Xiamen City, China: A modelling study

Objective

Mumps is a seasonal infectious disease, always occurring in winter and spring. In this study, we aim to analyze its epidemiological characteristics, transmissibility, and its correlation with meteorological variables.

Method

A seasonal Susceptible–Exposed–Infectious/Asymptomatic–Recovered model and a next-generation matrix method were applied to estimate the time-dependent reproduction number (R_t).

Results

The seasonal double peak of annual incidence was mainly in May to July and November to December. There was high transmission at the median of R_t = 1.091 (ranged: 0 to 4.393). R_t was seasonally distributed mainly from February to April and from September to November. Correlations were found between temperature (Pearson correlation coefficient [r] ranged: from 0.101 to 0.115), average relative humidity (r = 0.070), average local pressure (r = -0.066), and the number of new cases. In addition, average local pressure (r = 0.188), average wind speed (r = 0.111), air temperature (r ranged: -0.128 to -0.150), average relative humidity (r = -0.203) and sunshine duration (r = -0.075) were all correlated with R_t.

Conclusion

A relatively high level of transmissibility has been found in Xiamen City, leading to a continuous epidemic of mumps. Meteorological factors, especially air temperature and relative humidity, may be more closely associated with mumps than other factors.

Global Stability of a Mumps Transmission Model with Quarantine Measure

In this paper, a model of mumps transmission with quarantine measure is proposed and then the control reproduction numberℛ c of the model is obtained. This model admits a unique endemic equilibrium P* if and only if R c > 1, while the disease-free equilibrium P 0 always exists. By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem, we first show that the equilibrium P 0 is globally asymptotically stable (GAS) if R c ≤ 1; second, we prove that the equilibrium P* is GAS if R c > 1. Our results reveal that mumps can be eliminated from the community forℛ c ≤ 1 and it will be persistent forℛ c > 1 , and quarantine measure can also effectively control the mumps transmission.

Estimating the Transmissibility of Mumps: A Modelling Study in Wuhan City, China

Despite the adoption of a national immunization program in China, the incidence of mumps remains high. This study aimed to describe the epidemiological characteristics, including the time, region, occupation, and age, of mumps in Wuhan from 2005 to 2018 and to evaluate its transmissibility. In this study, the susceptible-exposed-infectious-asymptomatic-recovered (SEIAR) model fitted the actual incidence data of mumps. The effective reproduction number (R t ) was used to evaluate and compare the transmission capacity in different areas. From 2005 to 2018, there were 36,415 cases. The incidence of mumps was highest among people aged 5-10 years (460.02 per 100,000). The SEIAR model fitted the reported mumps data well (P < 0.01). The median transmissibility (R t ) was 1.04 (range = 0-2.50). There were two peak spreads every year (from March to May and from October to December). The R t peak always appeared in the first 2 months of the peak incidence rate. The peak time of the epidemic spread of mumps was 1-2 months earlier than the peak incidence rate. The prevention and control measures of vaccination for children aged 5-10 years should be taken before the peak transmission capacity each year, 2 months before the peak of the outbreak, to reduce the spread of mumps.

Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

We present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number [Formula: see text] as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If [Formula: see text] then the disease-free periodic solution is globally asymptotically stable, while if [Formula: see text] then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

Epidemiology of laboratory-confirmed mumps infections in South Africa, 2012-2017: a cross-sectional study

Background

Data on the burden of mumps in South Africa are limited and the epidemiology of mumps in this setting is not well understood. We present an analysis of mumps data in South Africa from 2012 to 2017.

Methods

This cross-sectional study included secondary data on laboratory-confirmed mumps infections from 2012 to 2017, archived at the South African National Health Laboratory Services’ data repository as well as from four private laboratories. Mumps-specific immunoglobulin M (IgM) and/or viral nucleic acid positive results represented acute infections. We used age-specific mid-year population estimates for each study year as denominators when calculating annual cumulative incidence. Seasonality was based on the season that showed a peak in infections.

Results

Out of 48,580 records obtained from the public and private sectors, 46,713 (96.2%) were from the private sector. Over the study period, there were 7494 acute infections, 7085 (94.5%) of which were recorded in the private sector. Of these 7494 infections, 3924 (52.4%) occurred in males. The proportion of samples tested that were IgM positive was 18.6% (1058/5682) in 2012, 15% (1016/6790) in 2013, 15.8% (1280/8093) in 2014, 15.5% (1384/8944) in 2015, 13.1% (1260/9629) in 2016 and 15.8% (1496/9442) in 2017. The cumulative incidence rate per 100,000 was highest in children between one and 9 years throughout the study period. The cumulative incidence of infections was highest in the Western Cape, Gauteng and the Northern Cape. Infections peaked in June and November.

Conclusion

Laboratory-confirmed mumps infections predominantly occurred in spring, affecting children below 10 years of age and individuals who were male. There were fewer tests performed in the public sector compared to the private sector. Since only laboratory data was analysed our results represent and underestimate of disease burden. Further studies that include clinical data are required to provide better estimates of disease burden in South Africa.

Assessing the Changes of Mumps Characteristics with Different Vaccination Strategies Using Surveillance Data: Importance to Introduce the 2-Dose Schedule in Quzhou of China

BACKGROUND

From 2005 to 2016, the prevention and control of mumps in China have undergone three stages of transition. These include the use of MuCV as a self-supported vaccine, the introduction of one-dose MMR to the Expanded Program on Immunization (EPI), and the administration of two-dose MuCV following supplementary immunization activities (SIAs) using MM. Here, using surveillance data, we assessed the epidemiology of mumps during the three stages.

METHODS

Children in Quzhou of China born from 2005 to 2016 and registered in the Zhejiang Provincial Immunization Information System (ZJIIS) were included. We analyzed the epidemic data and calculated incidence and MuCV coverage via birth cohorts.

RESULTS

The average incidence of mumps in 2005-2006, 2007-2010, and 2011-2016 was 51.57, 41.02, and 12.53 per 100,000 individuals, respectively. The highest incidence was in children aged 6-14 years from 2005-2016, of which the majority were school students (67.84%). Approximately 90% of the reported outbreaks occurred in school children (primary school/middle school). The seasonal characteristics of mumps were less obvious from 2011 to 2016. The coverage of one-dose MMR in the 2005 birth cohort was 71.38%. For the 2006-2010 birth cohort, the coverage of one-dose MuCV was 96.82% and the coverage of two-dose MuCV was 17.68%. The children born from 2011 to 2016 were only free vaccinated with MMR; the coverage of one-dose MuCV was 99.10%. The mumps incidence in the three birth cohorts significantly declined (X 2 = 805.90, P < 0.001 for trend). Except the children less than two years old, the mumps incidence for the children born from 2006 to 2010 was higher than that for the children born from 2011 to 2016.

CONCLUSION

The mumps incidence significantly declined following the introduction of one-dose MMR. The SIA using MM led to a rapid reduction of mumps cases. Therefore, we recommend a two-dose MuCV routine immunization schedule and improved vaccination coverage.

Effects of extreme meteorological factors on daily mumps cases in Hefei, China, during 2011-2016

Mumps remains one of the worldwide major health problems over the past decade. Seasonal variations of mumps indicate that meteorological factors play an important role in the development of mumps, but few studies have investigated the relationship between extreme meteorological factors and the incidence of mumps. Daily mumps cases and meteorological factors in Hefei, China, from 2011 to 2016 were obtained. A generalized additive model combined with the distributed lag nonlinear model (DLNM) was used to quantify the risk of extreme meteorological factors on mumps incidence. Nonlinear relationships were observed among all meteorological factors and mumps incidence. We found that extremely low and high temperatures increased the risk of mumps. The relative risks (RRs) of the cumulative effects along 30 lag days were 2.02 (95%CI: 1.14-3.56) and 2.42 (95%CI: 1.37-4.24), respectively. Both short and long sunshine duration had negative correlation on mumps, with cumulative RRs of 0.64 (95%CI: 0.46-0.92) and 0.57 (95%CI: 0.44-0.74), respectively. In the subgroup analysis, males were found to be more sensitive to extreme weather, especially extreme temperatures and sunshine duration. This study suggests that extreme meteorological factors, especially extreme temperatures and sunshine duration, exert a significant impact on the incidence of mumps. When formulating and implementing effective strategies to the prevention and control of mumps, authorities should take the effect caused by extreme meteorological factors into consideration and pay more attention to susceptible populations, such as male children and teenagers.

Modelling the Transmission Dynamics and Control of Mumps in Mainland China

Mumps is a common childhood viral disease and children have been vaccinated throughout the world since 1967. The incidence of mumps has increased with more than 300,000 young people infected with mumps annually in mainland China since 2005. Therefore, we designed and analyzed long-term mumps surveillance data in an SVEILR (susceptible-vaccinated-exposed-severely infectious-mildly infectious-recovered) dynamic transmission model with optimized parameter values to describe the dynamics of mumps infections in China. There were 18.02% of mumps infected young adults seeking medical advice. The vaccine coverage has been insufficient in China. Young adults with frequent contact and mild infection were identified as a major driver of mumps epidemics. The reproduction number of mumps was determined 4.28 in China. Sensitivity analysis of the basic reproduction number and the endemic equilibrium was conducted to evaluate the effectiveness of mumps control measures. We propose to increase the vaccine coverage and make two doses of MMR (Measles, mumps and rubella) vaccines freely available in China.