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This paper is devoted to a nonautonomous SVIR epidemic model with relapse, that is, the recurrence rate is considered in the model. The permanent of the system is proved, and the result on the existence and uniqueness of globally attractive almost periodic solution of this system is obtained by constructing a suitable Lyapunov function. Some analysis for the necessity of considering the recurrence rate in the model is also presented. Moreover, some examples and numerical simulations are given to show the feasibility of our main results. Through numerical simulation, we have obtained the influence of vaccination rate and recurrence rate on the spread of the disease. The conclusion is that in order to control the epidemic of infectious diseases, we should increase the vaccination rate while reducing the recurrence rate of the disease.

Different epidemic models with one or two characteristics of multi-group, age structure and spatial diffusion have been proposed, but few models take all three into consideration. In this paper, a novel multi-group SEIR epidemic model with both age structure and spatial diffusion is constructed for the first time ever to study the transmission dynamics of infectious diseases. We first analytically study the positivity, boundedness, existence and uniqueness of solution and the existence of compact global attractor of the associated solution semiflow. Based on some assumptions for parameters, we then show that the disease-free steady state is globally asymptotically stable by utilizing appropriate Lyapunov functionals and the LaSalle's invariance principle. By means of Perron-Frobenius theorem and graph-theoretical results, the existence and global stability of endemic steady state are ensured under appropriate conditions. Finally, feasibility of main theoretical results is showed with the aid of numerical examples for model with two groups which is important from the viewpoint of applications.

Background: In March 2009, pandemic influenza A(H1N1) (A(H1N1)pdm) emerged in Mexico and the United States. In Japan, since the first outbreak of A(H1N1)pdm in Osaka and Hyogo Prefectures occurred in the middle of May 2009, the virus had spread over 16 of 47 prefectures as of June 4, 2009. Methods/Principal Findings: We analyzed all-segment concatenated genome sequences of 75 isolates of A(H1N1)pdm viruses in Japan, and compared them with 163 full-genome sequences in the world. Two analyzing methods, distancebased and Bayesian coalescent MCMC inferences were adopted to elucidate an evolutionary relationship of the viruses in the world and Japan. Regardless of the method, the viruses in the world were classified into four distinct clusters with a few exceptions. Cluster 1 was originated earlier than cluster 2, while cluster 2 was more widely spread around the world. The other two clusters (clusters 1.2 and 1.3) were suggested to be distinct reassortants with different types of segment assortments. The viruses in Japan seemed to be a multiple origin, which were derived from approximately 28 transported cases. Twelve cases were associated with monophyletic groups consisting of Japanese viruses, which were referred to as micro-clade. While most of the micro-clades belonged to the cluster 2, the clade of the first cases of infection in Japan originated from cluster 1.2. Micro-clades of Osaka/Kobe and the Fukuoka cases, both of which were school-wide outbreaks, were eradicated. Time of most recent common ancestor (tMRCA) for each micro-clade demonstrated that some distinct viruses were transmitted in Japan between late May and early June, 2009, and appeared to spread nation-wide throughout summer. Conclusions: Our results suggest that many viruses were transmitted from abroad in late May 2009 irrespective of preventive actions against the pandemic influenza, and that the influenza A(H1N1)pdm had become a pandemic stage in June 2009 in Japan. [ABSTRACT FROM AUTHOR]

Objective We aimed to determine the burden of bacillary dysentery in China, its cross-regional variations, trends in morbidity and mortality, the causative bacterial species and antimicrobial resistance patterns. Methods We extracted and integrated governmental statistics and relevant medical literature published from 1991 to 2000. Data were also collected from one general hospital each for the six provinces and Jin-an district, Shanghai, representative of six geographical regions and a modern city. Findings In 2000, 0.8–1.7 million episodes of bacillary dysentery occurred of which 0.5 to 0.7 million were treated at health-care facilities and 0.15–0.20 million patients were hospitalized. The highest morbidity and mortality rates were among the youngest and oldest age groups. Bacillary dysentery peaked during the summer months. The major causative species was Shigella flexneri (86%) and the predominant S. flexneri serotype was 2a (80%). About 74–80% of Shigella isolates remained susceptible to fluorinated quinolones. Conclusion We conclude that while morbidity and mortality due to bacillary dysentery has decreased considerably in China in the past decade due to increasing access to affordable health care and antibiotics, a considerable burden exists among the youngest and oldest age groups and in regions with low economic development. We suggest that while a vaccine would be effective for short- and medium-term control of bacillary dysentery, improved water supply, sanitation, and hygiene are likely to be required for long-term control. [ABSTRACT FROM AUTHOR]