We perform a bifurcation analysis on an SIR model involving two pathogens that influences each other. Partial cross-immunity is assumed and coinfection is thought to be less transmittable then each of the diseases alone. The susceptible class has density dependent growth with carrying capacity $K$. Our model generalizes the model developed in our previous papers by introducing the possibility for coinfected individuals to spread only one of the diseases when in contact with a susceptible. We perform a bifurcation analysis and prove the existence of a branch of stable equilibrium points parmeterized by $K$. The branch bifurcates for some $K$ resulting in changes in which compartments are present as well as the overall dynamics of the system. Depending on the parameters different transition scenarios occur.

Abstract. It is essential to understand the dynamics of epidemics in the presence of coexisting pathogens. There are various phenomenon that can effect the dynamics. In this paper, we formulate a mathematical model using different assumptions to capture the effect of these additional phenomena such as partial cross immunity, density dependence in each class and a role of recovered population in the dynamics. We found the basic reproduction number for each model which is the threshold that describes the invasion of disease in population. The basic reproduction number in each model shows that the persistence of disease or strains depends on the carrying capacity. In the model of this paper, we present the local stability analysis of the boundary equilibrium points and observed that the recovered population is not uniformly bounded with respect to K.

We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number [Formula: see text] for time-independent and periodical models and establish the permanence dichotomy: if [Formula: see text], extinction on all patches is imminent, and if [Formula: see text], permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.

In this paper we study prey-predator relationship in the presence of prey species pool. We describe the set of parameters when the predator will survive and find the threshold when you lose predator survival. This is based on analysis of dependence of locally stable equilibrium points on the parameters of the problem especially on the predator natural mortality rate e. In particular we give an interval for e in terms of other parameters where predators survive. This can allow to control the survival of predators by certain actions to move certain parameters to a safe area. We discover also a more complicated dynamics for small mortality rate.

Bluetongue virus (BTV) serotype 8 has been circulating in Europe since a major outbreak occurred in 2006, causing economic losses to livestock farms. The unpredictability of the biting activity of midges that transmit BTV implies difficulty in computing accurate transmission models. This study uniquely integrates field collections of midges at a range of European latitudes (in Sweden, The Netherlands, and Italy), with a multi-scale modelling approach. We inferred the environmental factors that influence the dynamics of midge catching, and then directly linked predicted midge catches to BTV transmission dynamics. Catch predictions were linked to the observed prevalence amongst sentinel cattle during the 2007 BTV outbreak in The Netherlands using a dynamic transmission model. We were able to directly infer a scaling parameter between daily midge catch predictions and the true biting rate per cow per day. Compared to biting rate per cow per day the scaling parameter was around 50% of 24 h midge catches with traps. Extending the estimated biting rate across Europe, for different seasons and years, indicated that whilst intensity of transmission is expected to vary widely from herd to herd, around 95% of naïve herds in western Europe have been at risk of sustained transmission over the last 15 years.

In this paper we develop a compartmental model of SIR type (the abbreviation refers to the number of Susceptible, Infected and Recovered people) that models the population dynamics of two diseases that can coinfect. We discuss how the underlying dynamics depends on the carrying capacity K: from a simple dynamics to a more complex. This can also help in understanding the appearance of more complicated dynamics, for example, chaos and periodic oscillations, for large values of K. It is also presented that pathogens can invade in population and their invasion depends on the carrying capacity K which shows that the progression of disease in population depends on carrying capacity. More specifically, we establish all possible scenarios (the so-called transition diagrams) describing an evolution of an (always unique) locally stable equilibrium state (with only non-negative compartments) for fixed fundamental parameters (density independent transmission and vital rates) as a function of the carrying capacity K. An important implication of our results is the following important observation. Note that one can regard the value of K as the natural 'size' (the capacity) of a habitat. From this point of view, an isolation of individuals (the strategy which showed its efficiency for COVID-19 in various countries) into smaller resp. larger groups can be modelled by smaller resp. bigger values of K. Then we conclude that the infection dynamics becomes more complex for larger groups, as it fairly maybe expected for values of the reproduction number R0≈1 . We show even more, that for the values R0>1 there are several (in fact four different) distinguished scenarios where the infection complexity (the number of nonzero infected classes) arises with growing K. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra model considered previously in Ghersheen et al. (Math Meth Appl Sci 42(8), 2019).

In this paper we develop an SIR model for coinfection. We discuss how the underlying dynamics depends on the carrying capacity $K$: from a simple dynamics to a more complicated. This can help in understanding of appearance of more complicated dynamics, for example, chaos etc. The density dependent population growth is also considered. It is presented that pathogens can invade in population and their invasion depends on the carrying capacity $K$ which shows that the progression of disease in population depends on carrying capacity. Our approach is based on a bifurcation analysis which allows to generalize considerably the previous Lotka-Volterra type models.

We consider a tritrophic system with one basal and one top species and a large number of primary consumers, and derive upper and lower bounds for the total biomass of the middle trophic level. These estimates do not depend on dynamical regime, holding for fixed point, periodic, or chaotic dynamics. We have two kinds of estimates, depending on whether the predator abundance is zero. All these results are uniform in a self-limitation parameter, which regulates prey diversity in the system. For strong self-limitation, diversity is large; for weak self-limitation, it is small. Diversity depends on the variance of species' parameter values. The larger this variance, the lower the diversity, and vice versa. Moreover, variation in the parameters of the Holling type II functional response changes the bifurcation character, with the equilibrium state with nonzero predator abundance losing stability. If that variation is small then the bifurcation can lead to oscillations (the Hopf bifurcation). Under certain conditions, there exists a supercritical Hopf bifurcation. We then find a connection between diversity and Hopf bifurcations. We also show that the system exhibits top-down regulation and a hump-shaped diversity-productivity curve. We then extend the model by allowing species to experience self-regulation. For this extended model, explicit estimates of prey diversity are obtained. We study the dynamics of this system and find the following. First, diversity and system dynamics crucially depend on variation in species parameters. We show that under certain conditions, the system undergoes a supercritical Hopf bifurcation. We also establish a connection between diversity and Hopf bifurcations. For strong self-limitation, diversity is large and complex dynamics are absent. For weak self-limitation, diversity is small and the equilibrium with non-zero predator abundance is unstable.

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 (R-0) 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, R-0 was typically higher in FLAPS configurations, and the simulation study corroborated the pattern for later stages of outbreaks. Further, both R-0 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.

By simulations of population growth exposed to environmental noise, we compared realised long-run growth rate of age structured populations of four different life histories, with four approximations. One approximation used a non-structured population model, including specific population growth rates for each time step, determined by actual vital rates, while the other three used age-structured data to estimate a ‘mean’ growth rate, then applicable for all time steps. In general, approximations were reasonable accurate. Yet some were completely erroneous and inaccurate enough to move stationary populations to become species on the red list as an endangered species according to International Union for Conservation of Nature (IUNC). The inaccuracies depended, in the following decreasing order, on: life history, what part of the demography the noise was acting on, and noise colour. The non-structured growth approximation had smaller errors with red noise while the three age-structured approximations had their largest errors with red noise. Since it is generally understood that the most common noise in nature is red noise, we conclude that the non-structured approximation will be the best predictor of population growth in most cases. We also conclude that evenness in distribution over age classes is a possible predictor for the sensitivity of long-run growth rate to type of approximation and therefore a promising object for further studies. Finally, our results indicate that in general, more focus ought to be on reducing the error in the data collection on population densities, especially for studies over longer time periods, than of collecting age-specific data.

We develop a novel approach to study the global behaviour of large foodwebs for ecosystems where several species share multiple resources. The model extends and generalizes some previous works and takes into account self-limitation. Under certain explicit conditions, we establish the global convergence and persistence of solutions.

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.

The population size has far-reaching effects on the fitness of a population that in turn influences the population extinction or persistence. Understanding the density- and age-dependent factors will facilitate more accurate predictions about the population dynamics and its asymptotic behavior. In this paper, we develop a rigorous mathematical analysis of the study of positive and negative effects of the increased population density in the classical nonlinear age-structured population model. One of the main results expresses the global stability of the system in terms of the newborn function only. We establish the existence of a threshold population size implying the population extinction, which is well known in the population dynamics as the Allee effect.

Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection are important in this case. We formulated an susceptible infected recovered (SIR) model that describes the coinfection of the two viral strains in a single host population with an addition of limited growth of susceptible in terms of carrying capacity. The model describes five classes of a population: susceptible, infected by first virus, infected by second virus, infected by both viruses, and completely immune class. We proved that for any set of parameter values, there exists a globally stable equilibrium point. This guarantees that the disease always persists in the population with a deeper connection between the intensity of infection and carrying capacity of population. Increase in resources in terms of carrying capacity promotes the risk of infection, which may lead to destabilization of the population.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Culicoides species from the Obsoletus group are important vectors of bluetongue and Schmallenberg virus. This group consists of several species that cannot easily be identified using morphological characteristics. Therefore, limited information is available about their distribution and habitat preferences. In this study, we aimed to elucidate the species composition of the Obsoletus group in three habitat types at climatically different latitudes across Europe. Traps were placed in three habitat types in three countries at different latitudes. After DNA extraction, biting midges were identified using PCR and gel electrophoresis. Extraction of DNA using Chelex proved to be a cost and time efficient method for species identification. A latitudinal effect on the relative abundance of species from the Obsoletus group was found. Species composition was unique for most country-habitat combinations. The majority of biting midges were either C. obsoletus s.s. or C. scoticus, and both species were found at all latitudes and habitats. Their wide distribution and their high abundance at livestock farms make these species likely candidates for rapid farm-to-farm transmission of pathogens throughout Europe. Our results emphasize the need to differentiate Obsoletus group species to better understand their ecology and contribution to pathogen transmission.

Recycling essential plant nutrients like nitrogen (N), phosphorus (P), and potassium (K) from organic waste such as human and animal excreta will be an essential part of sustainable food systems and a circular economy. However, transportation is often cited as a major barrier to increased recycling as organic waste is heavy and bulky, and distances between areas of abundant waste may be far from areas with a need for fertilizers. We investigated the effect of increased input data spatial resolution to an optimization model on the weight, distance, and spatial patterns of transport. The model was run in Sweden and in Pakistan to examine cost-effectiveness of transporting excess excreta to areas of crop need after local recycling. Increasing the resolution of input data from political boundaries (municipalities and districts) to 0.083 decimal grids increased the amount of N requiring transport by 12% in Pakistan and increased P requiring transport by 14% in Sweden. The average distance decreased by 67% (to 44 km) in Pakistan but increased by 1 km in Sweden. Further increasing the resolution to 5 km grids in Sweden decreased the average transportation distance by 9 km (down to 123 km). In both countries, increasing resolution also decreased the number of long-distance heavy transports, and as such costs did not increase as much as total distance and weight transported. Ultimately, transportation in Pakistan seemed financially beneficial: the cost of transport only represented 13% of the NPK fertilizer value transported, and total recycling could even cover 78% of additional fertilizer purchases required. In Sweden, the cost of transporting excreta did not seem cost effective without valuing other potential benefits of increased recycling: costs were three times higher than the fertilizer value transported in excreta at the 5 km resolution. In summary, increasing input data resolution created a more realistic picture of recycling needs. This also highlighted more favorable cost to fertilizer value ratios which could make it easier to move forward with industry and government partners to facilitate productive recycling. Our analysis shows that in both countries increased recycling can result in better spatial nutrient balances.

The production of food can have large impacts on sustainable development in relation to various socio-ecological dimensions, like climate change, the environment, animal welfare, livestock epidemiology, and the economy. To achieve a sustainable food production system in Sweden, an integrated approach that considers all five of these dimensions, and all parts of the food production chain, is necessary. This paper systematically reviewed the literature related to food production in Sweden, especially in association with resource distribution and recycling logistics, and identified potential sustainability interventions and assessed their effects according to the five dimensions. Participation of stakeholders across the food production chain contributed with the focus of the literature search and subsequent synthesis. In general, there were synergies between the sustainability interventions and their effect on climate change and the environment, while there often were trade-offs between effects on the economy and the other dimensions. Few interventions considered effects on animal welfare or livestock epidemiology and few studies dealt with resource distribution and recycling logistics. This indicates that there is a need for future research that considers this in particular, as well as research that considers the whole food production chain and all dimensions at once, and investigates effects across multiple scales.

BACKGROUND:The outbreaks of bluetongue and Schmallenberg disease in Europe have increased efforts to understand the ecology of Culicoides biting midges and their role in pathogen transmission. However, most studies have focused on a specific habitat, region, or country. To facilitate wider comparisons, and to obtain a better understanding of the spread of disease through Europe, the present study focused on monitoring biting midge species diversity in three different habitat types and three countries across Europe.METHODS:Biting midges were trapped using Onderstepoort Veterinary Institute light traps at a total of 27 locations in Sweden, the Netherlands and Italy, comprising farm, peri-urban and wetland habitats. From July 2014 to June 2015 all locations were sampled monthly, except for during the winter months. Trapped midges were counted and identified morphologically. Indices on species richness, evenness and diversity were calculated. Community compositions were analysed using non-metric multidimensional scaling (NMDS) techniques.RESULTS:A total of 50,085 female midges were trapped during 442 collection nights. More than 88% of these belonged to the Obsoletus group. The highest midge diversity was found in Sweden, while species richness was highest in the Netherlands, and most specimens were trapped in Italy. For habitats within countries, diversity of the trapped midges was lowest for farms in all countries. Differences in biting midge species communities were more distinct across the three countries than the three habitat types.CONCLUSIONS:A core midge community could be identified, in which the Obsoletus group was the most abundant. Variations in vector communities across countries imply different patterns of disease spread throughout Europe. How specific species and their associated communities affect disease risk is still unclear. Our results emphasize the importance of midge diversity data at community level, how this differs across large geographic range within Europe, and its implications on assessing risks of midge-borne disease outbreaks.