Mathematical analysis of complex SIR model with coinfection and density dependence

An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed and several threshold conditions are obtained which describes the establishment of disease in the population. We prove that for small carrying capacity $K$ there exist a globally stable disease free equilibrium point. Furthermore, we establish the continuity of the transition dynamics of the stable equilibrium point, i.e. we prove that (1) for small values of $K$ there exists a unique globally stable equilibrium point, and (b) it moves continuously as $K$ is growing (while its face type may change). This indicate that carrying capacity is the crucial parameter and increase in resources in terms of carrying capacity promotes the risk of infection.Comment: 14 page

Influence on disease spread dynamics of herd characteristics in a structured livestock industry

Studies of between-herd contacts may provide important insight to disease transmission dynamics. By comparing the result from models with different levels of detail in the description of animal movement, we studied how factors influence the final epidemic size as well as the dynamic behaviour of an outbreak. We investigated the effect of contact heterogeneity of pig herds in Sweden due to herd size, between-herd distance and production type. Our comparative study suggests that the production-type structure is the most influential factor. Hence, our results imply that production type is the most important factor to obtain valid data for and include when modelling and analysing this system. The study also revealed that all included factors reduce the final epidemic size and also have yet more diverse effects on initial rate of disease spread. This implies that a large set of factors ought to be included to assess relevant predictions when modelling disease spread between herds. Furthermore, our results show that a more detailed model changes predictions regarding the variability in the outbreak dynamics and conclude that this is an important factor to consider in risk assessment

Biodiversity and robustness of large ecosystems

We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the global stability of solutions for systems with extinctions and large turnover rate. We show that when the extinction threshold is distinct from zero, the large time dynamics of system is fundamentally non-predictable. In the last part of the paper we obtain explicit analytical estimates of ecosystem robustness with respect to variations of resource supply which support the $R^*$ rule for a system with random parameters.Comment: 17 pages, 1 figure. To appear in Ecological Complexit

Realistic assumptions about spatial locations and clustering of premises matter for models of foot-and-mouth disease spread in the United States

Spatially explicit livestock disease models require demographic data for individual farms or premises. In the U.S., demographic data are only available aggregated at county or coarser scales, so disease models must rely on assumptions about how individual premises are distributed within counties. Here, we addressed the importance of realistic assumptions for this purpose. We compared modeling of foot and mouth disease (FMD) outbreaks using simple randomization of locations to premises configurations predicted by the Farm Location and Agricultural Production Simulator (FLAPS), which infers location based on features such as topography, land-cover, climate, and roads. We focused on three premises-level Susceptible-Exposed-Infectious-Removed models available from the literature, all using the same kernel approach but with different parameterizations and functional forms. By computing the basic reproductive number of the infection (R0) for both FLAPS and randomized configurations, we investigated how spatial locations and clustering of premises affects outbreak predictions. Further, we performed stochastic simulations to evaluate if identified differences were consistent for later stages of an outbreak. Using Ripley's K to quantify clustering, we found that FLAPS configurations were substantially more clustered at the scales relevant for the implemented models, leading to a higher frequency of nearby premises compared to randomized configurations. As a result, R0 was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R0 and simulations exhibited substantial spatial heterogeneity in terms of differences between configurations. Thus, using realistic assumptions when de-aggregating locations based on available data can have a pronounced effect on epidemiological predictions, affecting if, where, and to what extent FMD may invade the population. We conclude that methods such as FLAPS should be preferred over randomization approaches

Spatial and temporal investigations of reported movements, births and deaths of cattle and pigs in Sweden

<p>Abstract</p> <p>Background</p> <p>Livestock movements can affect the spread and control of contagious diseases and new data recording systems enable analysis of these movements. The results can be used for contingency planning, modelling of disease spread and design of disease control programs.</p> <p>Methods</p> <p>Data on the Swedish cattle and pig populations during the period July 2005 until June 2006 were obtained from databases held by the Swedish Board of Agriculture. Movements of cattle and pigs were investigated from geographical and temporal perspectives, births and deaths of cattle were investigated from a temporal perspective and the geographical distribution of holdings was also investigated.</p> <p>Results</p> <p>Most movements of cattle and pigs were to holdings within 100 km, but movements up to 1200 km occurred. Consequently, the majority of movements occurred within the same county or to adjacent counties. Approximately 54% of the cattle holdings and 45% of the pig holdings did not purchase any live animals. Seasonal variations in births and deaths of cattle were identified, with peaks in spring. Cattle movements peaked in spring and autumn. The maximum number of holdings within a 3 km radius of one holding was 45 for cattle and 23 for pigs, with large variations among counties. Missing data and reporting bias (digit preference) were detected in the data.</p> <p>Conclusion</p> <p>The databases are valuable tools in contact tracing. However since movements can be reported up to a week after the event and some data are missing they cannot replace other methods in the acute phase of an outbreak. We identified long distance transports of cattle and pigs, and these findings support an implementation of a total standstill in the country in the case of an outbreak of foot-and-mouth disease. The databases contain valuable information and improvements in data quality would make them even more useful.</p