Mathematical epidemiologic and simulation modelling of first wave COVID-19 in Malaysia.

Since the first coronavirus disease 2019 (COVID-19) outbreak appeared in Wuhan, mainland China on December 31, 2019, the geographical spread of the epidemic was swift. Malaysia is one of the countries that were hit substantially by the outbreak, particularly in the second wave. This study aims to simulate the infectious trend and trajectory of COVID-19 to understand the severity of the disease and determine the approximate number of days required for the trend to decline. The number of confirmed positive infectious cases [as reported by Ministry of Health, Malaysia (MOH)] were used from January 25, 2020 to March 31, 2020. This study simulated the infectious count for the same duration to assess the predictive capability of the Susceptible-Infectious-Recovered (SIR) model. The same model was used to project the simulation trajectory of confirmed positive infectious cases for 80 days from the beginning of the outbreak and extended the trajectory for another 30 days to obtain an overall picture of the severity of the disease in Malaysia. The transmission rate, ß also been utilized to predict the cumulative number of infectious individuals. Using the SIR model, the simulated infectious cases count obtained was not far from the actual count. The simulated trend was able to mimic the actual count and capture the actual spikes approximately. The infectious trajectory simulation for 80 days and the extended trajectory for 110 days depicts that the inclining trend has peaked and ended and will decline towards late April 2020. Furthermore, the predicted cumulative number of infectious individuals tallies with the preparations undertaken by the MOH. The simulation indicates the severity of COVID-19 disease in Malaysia, suggesting a peak of infectiousness in mid-March 2020 and a probable decline in late April 2020. Overall, the study findings indicate that outbreak control measures such as the Movement Control Order (MCO), social distancing and increased hygienic awareness is needed to control the transmission of the outbreak in Malaysia.

Temporal and spatial mapping of hand, foot and mouth disease in Sarawak, Malaysia.

Hand, foot and mouth disease (HFMD) is endemic in Sarawak, Malaysia. In this study, a geographical information system (GIS) was used to investigate the relationship between the reported HFMD cases and the spatial patterns in 11 districts of Sarawak from 2006 to 2012. Within this 7-years period, the highest number of reported HFMD cases occurred in 2006, followed by 2012, 2008, 2009, 2007, 2010 and 2011, in descending order. However, while there was no significant distribution pattern or clustering in the first part of the study period (2006 to 2011) based on Moran's I statistic, spatial autocorrelation (P = 0.068) was observed in 2012.

Genetic and environmental effects on age at menarche, and its relationship with reproductive health in twins.

INTRODUCTION: Menarche or first menstrual period is a landmark in reproductive life span and it is the most prominent change of puberty. The timing of menarche can be under the influence of genes as well as individual environmental factors interacting with genetic factors. OBJECTIVE: Our study objectives were (a) to investigate the heritability of age of menarche in twins, (b) to obtain the association between age of menarche and childhood factors, and reproductive events/behavior, (c) to examine whether or not having a male co-twin affects early/late menarche. METHODOLOGY: A group of female-female identical (n = 108, 54 pairs), non-identical twins (n = 68, 34 pairs) and 17 females from opposite-sex twin sets were identified from twin registries of Malaysia and Iran. Genetic analysis was performed via two methods of Falconers' formula and maximum likelihood. RESULTS: Heritability was found to be 66% using Falconers' formula and 15% using univariate twin analysis. Model analysis revealed that shared environmental factors have a major contribution in determining the age of menarche (82%) followed by non-shared environment (18%). DISCUSSION: Result of this study is consistent with that of the literature. Timing of menarche could be under the influence of shared and non-shared environmental effects. Hirsutism was found to have a higher frequency among subjects with late menarche. There was no significant difference in age of menarche between females of opposite-sex twins and females of same-sex twins. CONCLUSION: It is concluded that twin models provide a powerful means of examining the total genetic contribution to age of menarche. Longitudinal studies of twins may clarify the type of environmental effects that determine the age of menarche.

A climate distribution model of malaria transmission in Sudan.

Malaria remains a major health problem in Sudan. With a population exceeding 39 million, there are around 7.5 million cases and 35,000 deaths every year. The predicted distribution of malaria derived from climate factors such as maximum and minimum temperatures, rainfall and relative humidity was compared with the actual number of malaria cases in Sudan for the period 2004 to 2010. The predictive calculations were done by fuzzy logic suitability (FLS) applied to the numerical distribution of malaria transmission based on the life cycle characteristics of the Anopheles mosquito accounting for the impact of climate factors on malaria transmission. This information is visualized as a series of maps (presented in video format) using a geographical information systems (GIS) approach. The climate factors were found to be suitable for malaria transmission in the period of May to October, whereas the actual case rates of malaria were high from June to November indicating a positive correlation. While comparisons between the prediction model for June and the case rate model for July did not show a high degree of association (18%), the results later in the year were better, reaching the highest level (55%) for October prediction and November case rate.

The heritability of premenstrual syndrome.

We aimed to determine (1) the prevalence of premenstrual syndrome in a sample of twins and (2) the relative contribution of genes and environment in premenstrual syndrome. A group of 193 subjects inclusive of same gender twins (n = 176) and females from opposite sex twin sets (n = 17) entered the study. Heritability analysis used same gender twin data only. The probandwise concordance rate for the presence or absence of premenstrual syndrome was calculated and the heritability of premenstrual syndrome was assessed by a quantitative genetic model fitting approach using MX software. The prevalence of premenstrual syndrome was 43.0% and 46.8% in monozygotic and dizygotic twins, respectively. The probandwise concordance for premenstrual syndrome was higher in monozygotic (0.81) than in dizygotic twins (0.67), indicating a strong genetic effect. Quantitative genetic modeling found that a model comprising of additive genetic (A) and unique environment (E) factors provided the best fit (A: 95%, E: 5%). No association was found between premenstrual symptom and the following variables: belonging to the opposite gender twin set, birth weight, being breast fed and vaccination. These results established a clear genetic influence in premenstrual syndrome.

Novel bivariate moment-closure approximations.

Nonlinear stochastic models are typically intractable to analytic solutions and hence, moment-closure schemes are used to provide approximations to these models. Existing closure approximations are often unable to describe transient aspects caused by extinction behaviour in a stochastic process. Recent work has tackled this problem in the univariate case. In this study, we address this problem by introducing novel bivariate moment-closure methods based on mixture distributions. Novel closure approximations are developed, based on the beta-binomial, zero-modified distributions and the log-Normal, designed to capture the behaviour of the stochastic SIS model with varying population size, around the threshold between persistence and extinction of disease. The idea of conditional dependence between variables of interest underlies these mixture approximations. In the first approximation, we assume that the distribution of infectives (I) conditional on population size (N) is governed by the beta-binomial and for the second form, we assume that I is governed by zero-modified beta-binomial distribution where in either case N follows a log-Normal distribution. We analyse the impact of coupling and inter-dependency between population variables on the behaviour of the approximations developed. Thus, the approximations are applied in two situations in the case of the SIS model where: (1) the death rate is independent of disease status; and (2) the death rate is disease-dependent. Comparison with simulation shows that these mixture approximations are able to predict disease extinction behaviour and describe transient aspects of the process.

Novel moment closure approximations in stochastic epidemics.

Moment closure approximations are used to provide analytic approximations to non-linear stochastic population models. They often provide insights into model behaviour and help validate simulation results. However, existing closure schemes typically fail in situations where the population distribution is highly skewed or extinctions occur. In this study we address these problems by introducing novel second- and third-order moment closure approximations which we apply to the stochastic SI and SIS epidemic models. In the case of the SI model, which has a highly skewed distribution of infection, we develop a second-order approximation based on the beta-binomial distribution. In addition, a closure approximation based on mixture distribution is developed in order to capture the behaviour of the stochastic SIS model around the threshold between persistence and extinction. This mixture approximation comprises a probability distribution designed to capture the quasi-equilibrium probabilities of the system and a probability mass at 0 which represents the probability of extinction. Two third-order versions of this mixture approximation are considered in which the log-normal and the beta-binomial are used to model the quasi-equilibrium distribution. Comparison with simulation results shows: (1) the beta-binomial approximation is flexible in shape and matches the skewness predicted by simulation as shown by the stochastic SI model and (2) mixture approximations are able to predict transient and extinction behaviour as shown by the stochastic SIS model, in marked contrast with existing approaches. We also apply our mixture approximation to approximate a likelihood function and carry out point and interval parameter estimation.