Epidemiological model of diarrhoeal diseases and its application in prevention and control

Modelling the dynamics of direct and pathogens-induced dysentery diarrhoea epidemic with controls

In this paper, the dysentery dynamics model with controls is theoretically investigated using the stability theory of differential equations. The system is considered as SIRSB deterministic compartmental model with treatment and sanitation. A threshold number R0 is obtained such that R0≤ 1 indicates the possibility of dysentery eradication in the community while R0>1 represents uniform persistence of the disease. The Lyapunov-LaSalle method is used to prove the global stability of the disease-free equilibrium. Moreover, the geometric approach method is used to obtain the sufficient condition for the global stability of the unique endemic equilibrium for R0>1 . Numerical simulation is performed to justify the analytical results. Graphical results are presented and discussed quantitatively. It is found out that the aggravation of the disease can be decreased by using the constant controls treatment and sanitation.

A mathematical model of the indirect effects of rotavirus vaccination

Rotavirus (RV) infections progressively confer natural immunity against subsequent infection. Similarly to natural infection, vaccination with a live attenuated vaccine potentially reduces RV transmission and induces herd protection. A mathematical transmission model was developed to project the impact of a vaccination programme on the incidence of RV infection and disease for five countries in the European Union. With vaccination coverage rates of 70%, 90% and 95% the model predicted that, in addition to the direct effect of vaccination, herd protection induced a reduction in RV-related gastroenteritis (GE) incidence of 25%, 22% and 20%, respectively, for RV-GE of any severity, and of 19%, 15%, and 13%, respectively, for moderate-to-severe RV-GE, 5 years after implementation of a vaccination programme.

Development of a travelers' diarrhea vaccine for the military: how much is an ounce of prevention really worth?

Infectious diarrhea is one of the many threats to the deployed military, and given limited resources, a decision to pursue a vaccine acquisition strategy should be based on best evidence that weighs costs and benefits compared to alternatives. An economic model was developed to estimate the marginal cost to avert a duty day lost due to diarrhea for a vaccine acquisition strategy compared to current clinical management, for both multiplex and pathogen-specific vaccines. Vaccines against Campylobacter and enterotoxigenic Escherichia coli appeared to be more favorable than a Shigella vaccine. This model provides an evidence-based decision tool to support prioritization in vaccine development.

Scaling properties and symmetrical patterns in the epidemiology of rotavirus infection

The rich epidemiological database of the incidence of rotavirus, as a cause of severe diarrhoea in young children, coupled with knowledge of the natural history of the infection, can make this virus a paradigm for studies of epidemic dynamics. The cyclic recurrence of childhood rotavirus epidemics in unvaccinated populations provides one of the best documented phenomena in population dynamics. This paper makes use of epidemiological data on rotavirus infection in young children admitted to hospital in Melbourne, Australia from 1977 to 2000. Several mathematical methods were used to characterize the overall dynamics of rotavirus infections as a whole and individually as serotypes G1, G2, G3, G4 and G9. These mathematical methods are as follows: seasonal autoregressive integrated moving-average (SARIMA) models, power spectral density (PSD), higher-order spectral analysis (HOSA) (bispectrum estimation and quadratic phase coupling (QPC)), detrended fluctuation analysis (DFA), wavelet analysis (WA) and a surrogate data analysis technique. Each of these techniques revealed different dynamic aspects of rotavirus epidemiology. In particular, we confirm the existence of an annual, biannual and a quinquennial period but additionally we found other embedded cycles (e.g. ca. 3 years). There seems to be an overall unique geometric and dynamic structure of the data despite the apparent changes in the dynamics of the last years. The inherent dynamics seems to be conserved regardless of the emergence of new serotypes, the re-emergence of old serotypes or the transient disappearance of a particular serotype. More importantly, the dynamics of all serotypes is multiple synchronized so that they behave as a single entity at the epidemic level. Overall, the whole dynamics follow a scale-free power-law fractal scaling behaviour. We found that there are three different scaling regions in the time-series, suggesting that processes influencing the epidemic dynamics of rotavirus over less than 12 months differ from those that operate between 1 and ca. 3 years, as well as those between 3 and ca. 5 years. To discard the possibility that the observed patterns could be due to artefacts, we applied a surrogate data analysis technique which enabled us to discern if only random components or linear features of the incidence of rotavirus contribute to its dynamics. The global dynamics of the epidemic is portrayed by wavelet-based incidence analysis. The resulting wavelet transform of the incidence of rotavirus crisply reveals a repeating pattern over time that looks similar on many scales (a property called self-similarity). Both the self-similar behaviour and the absence of a single characteristic scale of the power-law fractal-like scaling of the incidence of rotavirus infection imply that there is not a universal inherently more virulent serotype to which severe gastroenteritis can uniquely be ascribed.