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Between 1990 and 1999, at Rekomitjie Research Station, Zambezi Valley, Zimbabwe, 29,360 female G. pallidipes were dissected to determine their ovarian category and trypanosome infection status. Overall prevalences were 3.45 and 2.66% for T. vivax and T. congolense , respectively, declining during each year as temperatures increased from July – December. Fits to age-prevalence data using Susceptible-Exposed-Infective (SEI) and SI compartmental models were statistically better than those obtained using a published catalytic model, which made the unrealistic assumption that no female tsetse survived more than seven ovulations. The improved models require knowledge of fly mortality, estimated separately from ovarian category distributions. Infection rates were not significantly higher for T. vivax than for T. congolense. For T. congolense in field-sampled female G. pallidipes , we found no statistical support for a model where the force of infection was higher at the first feed than subsequently. The long survival of adult female tsetse, combined with feeding at intervals ≤3 days, ensures that post-teneral feeds, rather than the first feed, play the dominant role in the epidemiology of T. congolense infections in G. pallidipes. This is supported by estimates that only about 3% of wild hosts at Rekomitjie were harbouring sufficient T. congolense to ensure that tsetse feeding off them take an infected meal, so that the probability of ingesting an infected meal is low at every meal. [ABSTRACT FROM AUTHOR]

This paper focuses on the long time dynamics for a class stochastic SEI model with standard incidence and infectivity in incubation period. Firstly, we investigate a unique global positive solution almost surely for any positive initial value. Secondly, we obtain a unique stationary measure and the extinction condition of the epidemic based on the technique of Lyapunov function and inequalities. Thirdly, we explore the asymptotic behavior of the solutions around equilibriums of the corresponding deterministic model from different aspects. Finally, we establish some numerical simulations to illustrate the main presented results.

Airborne pandemics have caused millions of deaths worldwide, large-scale economic losses, and catastrophic sociological shifts in human history. Researchers have developed multiple mathematical models and computational frameworks to investigate and predict pandemic spread on various levels and scales such as countries, cities, large social events, and even buildings. However, attempts of modeling airborne pandemic dynamics on the smallest scale, a single room, have been mostly neglected. As time indoors increases due to global urbanization processes, more infections occur in shared rooms. In this study, a high-resolution spatio-temporal epidemiological model with airflow dynamics to evaluate airborne pandemic spread is proposed. The model is implemented, using Python, with high-resolution 3D data obtained from a light detection and ranging (LiDAR) device and computing model based on the Computational Fluid Dynamics (CFD) model for the airflow and the Susceptible–Exposed–Infected (SEI) model for the epidemiological dynamics. The pandemic spread is evaluated in four types of rooms, showing significant differences even for a short exposure duration. We show that the room's topology and individual distribution in the room define the ability of air ventilation to reduce pandemic spread throughout breathing zone infection. [ABSTRACT FROM AUTHOR]

Mathematical model of the spread of a virus in trains which considers transmission of infection from two types of sick passengers (clearly infected and latently infected) was built and named SEI (Susceptible-Exposed-Infected) model. Ventilation and movements of the passengers inside the train are considered through the porous medium equation. An algorithm for filling empty seats in the train is developed. A route of ten hours duration with two stop stations was simulated. The results of numerical calculations allow to conclude that asymptomatic infected passengers are the most dangerous group in the spread of infection. [ABSTRACT FROM AUTHOR]

In order to explore the impact of the growth rate of the habitat on the transmission of rabies, we consider a SEI model for fox rabies on a growing spatial domain. The basic reproduction number is introduced using the next infection operator, spectral analysis and the corresponding eigenvalue problem. The stability of equilibria is also established using the upper and lower solutions method in terms of this number. Our results show that a large growth rate of the domain has a negative impact on the prevention and control of rabies. Numerical simulations are presented to verify our theoretical results.

In this paper, the global dynamics of an SEIepidemic model with constant immigration and general nonlinear incidence function is investigated. It is shown that there is neither a disease free equilibrium nor a basic reproduction number for this kind of models containing immigration terms. Moreover, the existence of a unique endemic equilibrium is proved. Using second Lyapunov method, we establish the global stability of the positive equilibrium. For a specific type of incidence function, some numerical simulations are presented to validate the theoretical results.

Assessing the performance of a surveillance system for infectious diseases of domestic animals is a challenging task for health authorities. Therefore, it is important to assess what strategy is the most effective in identifying the onset of an epidemic and in minimizing the number of infected farms. The aim of the present work was to evaluate the performance of the bovine tuberculosis (bTB) surveillance system in the network of dairy farms in the Emilia-Romagna (ER) Region, Italy. A bTB-free Region since 2007, ER implements an integrated surveillance strategy based on three components, namely routine on-farm tuberculin skin-testing performed every 3 years, tuberculin skin-testing of cattle exchanged between farms, and post-mortem inspection at slaughterhouses. We assessed the effectiveness of surveillance by means of a stochastic network model of both within-farm and between-farm bTB dynamics calibrated on data available for ER dairy farms. Epidemic dynamics were simulated for five scenarios: the current ER surveillance system, a no surveillance scenario that we used as the benchmark to characterize epidemic dynamics, three additional scenarios in which one of the surveillance components was removed at a time so as to outline its significance in detecting the infection. For each scenario we ran Monte Carlo simulations of bTB epidemics following the random introduction of an infected individual in the network. System performances were assessed through the comparative analysis of a number of statistics, including the time required for epidemic detection and the total number of infected farms during the epidemic. Our analysis showed that slaughterhouse inspection is the most effective surveillance component in reducing the time for disease detection, while routine surveillance in reducing the number of multi-farms epidemics. On the other hand, testing exchanged cattle improved the performance of the surveillance system only marginally.

We have developed a dynamic epidemiological model informed by records of viral presence and genotypes to evaluate potential transmission routes maintaining a viral pathogen in economically and culturally important anadromous fish populations. In the Columbia River Basin, infectious hematopoietic necrosis virus (IHNV) causes severe disease, predominantly in juvenile steelhead trout ( Oncorhynchus mykiss ) and less frequently in Chinook salmon ( O. tshawytscha ). Mortality events following IHNV infection can be devastating for individual hatchery programs. Despite reports of high local mortality and extensive surveillance efforts, there are questions about how viral transmission is maintained. Modeling this system offers important insights into disease transmission in natural aquatic systems, as well as about the data requirements for generating accurate estimates about transmission routes and infection probabilities. We simulated six scenarios in which testing rates and the relative importance of different transmission routes varied. The simulations demonstrated that the model accurately identified routes of transmission and inferred infection probabilities accurately when there was testing of all cohort-sites. When testing records were incomplete, the model accurately inferred which transmission routes exposed particular cohort-sites but generated biased infection probabilities given exposure. After validating the model and generating guidelines for result interpretation, we applied the model to data from 14 annual cohorts (2000–2013) at 24 focal sites in a sub-region of the Columbia River Basin, the lower Columbia River (LCR), to quantify the relative importance of potential transmission routes in this focal sub-region. We demonstrate that exposure to IHNV via the return migration of adult fish is an important route for maintaining IHNV in the LCR sub-region, and the probability of infection following this exposure was relatively high at 0.16. Although only 1% of cohort-sites experienced self-exposure by infected juvenile fish, this transmission route had the greatest probability of infection (0.22). Increased testing and/or determining whether transmission can occur from cohort-sites without testing records (e.g., determining there was no testing record because there were no fish at the cohort-site) are expected to improve inference about infection probabilities. Increased use of secure water supplies and continued use of biosecurity protocols may reduce IHNV transmission from adult fish and juvenile fish within the site, respectively, to juvenile salmonids at hatcheries. Models and conclusions from this study are potentially relevant to understanding the relative importance of transmission routes for other important aquatic pathogens in salmonids, including the agents of bacterial kidney disease and coldwater disease, and the basic approach may be useful for other pathogens and hosts in other geographic regions. [ABSTRACT FROM AUTHOR]

Invasive species raise concern around the globe, and much empirical and theoretical research effort has been devoted to their management. Integrodifference equations are theoretical tools that have been used to understand the spatiotemporal process of a species invasion, with the potential to yield insight into the possible biological control measures. We develop a system of integrodifference equations to explore the potential release of a castrating barnacle parasite Sacculina carcini to control spread and abundance of an invasive species, Carcinus maenas, the European green crab. We find that the parasite does not completely eradicate the green crab population, but has the potential to reduce its density. Our model suggests that the crab population is likely to outrun the spread of the parasite, causing two waves of invasion travelling at different speeds. By performing a sensitivity analysis, we investigate the effects of the demographic parameters on the speed of invasion. To conclude, we discuss the predicted outcomes for the European green crab, and other non-target hosts, of using the castrating barnacle as a biocontrol agent. [ABSTRACT FROM AUTHOR]

Assessing the performance of a surveillance system for infectious diseases of domestic animals is a challenging task for health authorities. Therefore, it is important to assess what strategy is the most effective in identifying the onset of an epidemic and in minimizing the number of infected farms. The aim of the present work was to evaluate the performance of the bovine tuberculosis (bTB) surveillance system in the network of dairy farms in the Emilia-Romagna (ER) Region, Italy. A bTB-free Region since 2007, ER implements an integrated surveillance strategy based on three components, namely routine on-farm tuberculin skin-testing performed every 3 years, tuberculin skin-testing of cattle exchanged between farms, and post-mortem inspection at slaughterhouses. We assessed the effectiveness of surveillance by means of a stochastic network model of both within-farm and between-farm bTB dynamics calibrated on data available for ER dairy farms. Epidemic dynamics were simulated for five scenarios: the current ER surveillance system, a no surveillance scenario that we used as the benchmark to characterize epidemic dynamics, three additional scenarios in which one of the surveillance components was removed at a time so as to outline its significance in detecting the infection. For each scenario we ran Monte Carlo simulations of bTB epidemics following the random introduction of an infected individual in the network. System performances were assessed through the comparative analysis of a number of statistics, including the time required for epidemic detection and the total number of infected farms during the epidemic. Our analysis showed that slaughterhouse inspection is the most effective surveillance component in reducing the time for disease detection, while routine surveillance in reducing the number of multi-farms epidemics. On the other hand, testing exchanged cattle improved the performance of the surveillance system only marginally. [ABSTRACT FROM AUTHOR]

Abstract: An SEI epidemic model with constant recruitment and infectious force in the latent period is investigated. This model describes the transmission of diseases such as SARS. The behavior of positive solutions to a reaction–diffusion system with homogeneous Neumann boundary conditions are investigated. Sufficient conditions for the local and global asymptotical stability are given by linearization and by the method of upper and lower solutions and its associated monotone iterations. Our result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small. [Copyright &y& Elsevier]

Abstract: A number of wildlife pathogens are generalist and can affect different host species characterized by a wide range of body sizes. In this work we analyze the role of allometric scaling of host vital and epidemiological rates in a Susceptible-Exposed-Infected (SEI) model. Our analysis shows that the transmission coefficient threshold for the disease to establish in the population scales allometrically (exponent = 0.45) with host size as well as the threshold at which limit cycles occur. In contrast, the threshold of the basic reproduction number for sustained oscillations to occur is independent of the host size and is always greater than 5. In the case of rabies, we show that the oscillation periods predicted by the model match those observed in the field for a wide range of host sizes. The population dynamics of the SEI model is also analyzed in the case of pathogens affecting multiple coexisting hosts with different body sizes. Our analyses show that the basic reproduction number for limit cycles to occur depends on the ratio between host sizes, that the oscillation period in a multihost community is set by the smaller species dynamics, and that intermediate interspecific disease transmission can stabilize the epidemic occurrence in wildlife communities. [Copyright &y& Elsevier]

In this paper, we propose a generalized SEI epidemic model with a general nonlinear incidence rate and death rate functions. Furthermore, we consider that those who spread the disease are the infected and the exposed. Applying the direct Lyapunov method, we prove that the endemic equilibrium is globally asymptotically stable when the basic reproduction number R 0 is greater than unity and the disease free equilibrium is globally asymptotically stable when R 0 is lower than unity. We conclude that in order to obtain global stability and uniqueness of the equilibrium points, monoticity is necessary but not differentiability in the functions present in the model. [ABSTRACT FROM AUTHOR]

In this paper, the global dynamics of an S E I epidemic model with constant immigration and general nonlinear incidence function is investigated. It is shown that there is neither a disease free equilibrium nor a basic reproduction number for this kind of models containing immigration terms. Moreover, the existence of a unique endemic equilibrium is proved. Using second Lyapunov method, we establish the global stability of the positive equilibrium. For a specific type of incidence function, some numerical simulations are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

We develop a three dimensional compartmental model to investigate the impact of media coverage to the spread and control of infectious diseases (such as SARS) in a given region/area. Stability analysis of the model shows that the disease-free equilibrium is globally-asymptotically stable if a certain threshold quantity, the basic reproduction number (), is less than unity. On the other hand, if , it is shown that a unique endemic equilibrium appears and a Hopf bifurcation can occur which causes oscillatory phenomena. The model may have up to three positive equilibria. Numerical simulations suggest that when and the media impact is stronger enough, the model exhibits multiple positive equilibria which poses challenge to the prediction and control of the outbreaks of infectious diseases., (© Springer Science+Business Media, LLC 2007.)