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| 2. |
- Akram, Usman, 1984-
(författare)
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Closing nutrient cycles
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Adequate and balanced crop nutrition – with nitrogen (N), phosphorus (P), and potassium (K) – is vital for sustainable crop production. Inadequate and imbalanced crop nutrition contributes to the crop yield gaps – a difference in actual and potential crop yield. Yield gap is one of the many causes of insufficient food production, thus aggravating hunger and malnourishment across the globe. On the other hand, an oversupply of nutrients is highly unsustainable, in terms of both resource conservation and global environmental health. A decreasing excreta recycling in crop production is one of the many reasons for nutrient imbalances in agriculture. Previous studies show that increasing agricultural specialization leads to spatial separation of crop and animal production. Increasing distance between excreta production and crop needs is one of the leading factors that cause reduced excreta recycling. Studies focusing on excreta recycling show that a substantial barrier to a more efficient excreta nutrient reuse is the expensive transportation of bulky volumes of excreta over long distances. In order to overcome that barrier, more detailed spatial estimates of distances between excreta production and crop nutrient needs, and the associated costs for complete excreta transport in an entire country are needed. Hence, the overall aim of this thesis was to quantify the amount of nutrients in the excreta resources compared to the crop nutrient needs at multiple scales (global, national, subnational, and local), and to analyze the need for excreta transports, total distances and costs, to meet the crop nutrient needs in a country.On the global scale, annual (2000-2016) excreta supply (livestock and human) could provide at least 48% of N, 57% of P, and 81% of K crop needs. Although excreta supply was not enough to cover the annual crop nutrient needs at the global scale, at least 29 countries for N, 41 for P, and 71 for K had an excreta nutrient surplus. When including the annual use of synthetic fertilizers, at least 42 additional countries had a N surplus, with the equivalent figures for P being 17 countries, whereas 8 additional countries attained a K surplus. At the same time, when accounting for the use of synthetic fertilizers, each year, at least 57 countries had an N deficit, 70 a P deficit, and 51 countries a K deficit, in total equivalent to 14% of global N and 16% of each P and K crop needs. The total surplus in other countries during the period was always higher than the deficit in the countries with net nutrient deficits, except for P for some years. Unfortunately, both the deficits of the deficit countries and surpluses of the surplus countries were increasing substantially during the 17 years. Such global divergence in nutrient deficits and surpluses have clear implications for global food security and environmental health.A district-scale investigation of Pakistan showed that the country had a national deficit of 0.62 million tons of P and 0.59 million tons of K, but an oversupply of N. The spatial separation was not significant at this resolution; only 6% of the excreta N supply needed to be transported between districts. Recycling all excreta, within and between districts, could cut the use of synthetic N to 43% of its current use and eliminate the need for synthetic K, but there would be an additional need of 0.28 million tons of synthetic P to meet the crop nutrient needs in the entire country. The need for synthetic fertilizers to supplement the recycled excreta nutrients would cost USD 2.77 billion. However, it might not be prohibitively expensive to correct for P deficiencies because of the savings on the costs of synthetic N, and K. Excreta recycling could promote balanced crop nutrition at the national scale in Pakistan, which in turn could eliminate the nutrient-related crop yield gaps in the country.The municipal-scale investigation using Swedish data showed that the country had a national oversupply of 110,000 tons of N, 6,000 tons of P, and 76,000 tons of K. Excreta could provide up to 75% of N and 81% of P, and more than 100% of the K crop needs in the country. The spatial separation was pronounced at the municipal scale in the country. Just 40% of the municipalities produced over 50% of the excreta N and P. Nutrient balance calculations showed that excreta recycling within municipalities could provide 63% of the P crop needs. Another 18% of the P crop needs must be transported from surplus municipalities to deficit municipalities. Nationally, an optimized reallocation of surplus excreta P towards the P deficit municipalities would cost USD 192 million for a total of 24,079 km truck transports. The cost was 3.7 times more than the total NPK fertilizer value transported, and that met the crop nutrient needs. It was concluded that Sweden could potentially reduce its dependence on synthetic fertilizers, but to cover the costs of an improved excreta reuse would require valuing the additional benefits of recycling.An investigation was also done to understand the effect of the input data resolution on the results (transport needs and distances) from a model to optimize excreta redistribution. The results showed that the need for excreta transports, distances, and spatial patterns of the excreta transports changed. Increasing resolution of the spatial data, from political boundaries in Sweden and Pakistan to 0.083 decimal grids (approximately 10 km by 10 km at the equator), showed that transport needs for excreta-N increased by 12% in Pakistan, and the transport needs for excreta-P increased by 14% in Sweden. The effect of the increased resolution on transport analysis showed inconsistency in terms of the excreta total nutrient transportation distance; the average distance decreased by 67% (to 44 km) in Pakistan but increased by 1 km in Sweden. A further increase in the data resolution to 5 km by 5 km grids for Sweden showed that the average transportation distance decreased by 9 km. In both countries, increasing input data resolution resulted in a more favorable cost to fertilizer value ratios. In Pakistan, the cost of transport was only 13% of the NPK fertilizer value transported at a higher resolution. In Sweden, the costs decreased from 3.7 (at the political resolution) to slightly higher than three times of the fertilizer value transported in excreta at the higher data resolution.This Ph.D. thesis shows that we could potentially reduce the total use of synthetic fertilizers in the world and still reduce the yield gaps if we can create a more efficient recycling of nutrients both within and between countries, and a more demand adapted use of synthetic fertilizers.
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| 3. |
- Akram, Usman, 1984-, et al.
(författare)
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Closing Pakistan’s yield gaps through nutrient recycling
- 2018
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Ingår i: Frontiers in Sustainable Food Systems. - : Frontiers Media S.A.. - 2571-581X. ; , s. 1-14
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Tidskriftsartikel (refereegranskat)abstract
- Achieving food security will require closing yield gaps in many regions, including Pakistan. Although fertilizer subsidies have facilitated increased nitrogen (N) application rates, many staple crop yields have yet to reach their maximum potential. Considering that current animal manure and human excreta (bio-supply) recycling rates are low, there is substantial potential to increase the reuse of nutrients in bio-supply. We quantified 2010 crop N, phosphorus (P), and potassium (K) needs along with bio-supply nutrient availability for Pakistani districts, and compared these values to synthetic fertilizer use and costs. We found that synthetic fertilizer use combined with low bio-supply recycling resulted in a substantial gap between nutrient supply and P and K crop needs, which would cost 3 billion USD to fill with synthetic fertilizers. If all bio-supply was recycled, it could eliminate K synthetic fertilizer needs and decrease N synthetic fertilizer needs to 43% of what was purchased in 2010. Under a full recycling scenario, farmers would still require an additional 0.28 million tons of synthetic P fertilizers, costing 2.77 billion USD. However, it may not be prohibitively expensive to correct P deficiencies. Pakistan already spends this amount of money on fertilizers. If funds used for synthetic N were reallocated to synthetic P purchases in a full bio-supply recycling scenario, crop needs could be met. Most recycling could happen within districts, with only 6% of bio-supply requiring between-district transport when optimized to meet national N crop needs. Increased recycling in Pakistan could be a viable way to decrease yield gaps.
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| 4. |
- Andersson, Jonathan, 1992-
(författare)
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Bifurcations and Exchange of Stability with Density Dependence in a Coinfection Model and an Age-structured Population Model
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In nature many pathogens and in particular strains of pathogens with negative effects on species coexists. This is for simplicity often ignored in many epidemiological models. It is however still of interest to get a deeper understanding how this coexistence affects the dynamics of the disease. There are several ways at which coexistence can influence the dynamics. Coinfection which is the simultaneous infection of two or more pathogens can cause increased detrimental health effects on the host. Pathogens can also limit each others growth by the effect of cross immunity as well as promoting isolation. On the contrary one pathogen can also aid another by making the host more vulnerable to as well as more inclined to spread disease.Spread of disease is dependent on the density of the population. If a pathogen is able to spread or not, is strongly correlated with how many times individuals interact with each other. This in turn depends on how many individuals live in a given area. The aim of papers I-III is to provide an understanding how different factors including the carrying capacity of the host population affect the dynamics of two coexisting diseases. In papers I-III we investigate how the parameters effects the long term solution in the form of a stable equilibrium point. In particular we want to provide an understanding of how changes in the carrying capacity affects the long term existence of each disease as well as the occurrence of coinfection.The model that is studied in papers I-III is a generalization of the standard susceptible, infected, recovered (SIR) compartmental model. The SIR model is generalized by the introduction of the second infected compartment as well as the coinfection compartment. We also use a logistic growth term à la Verhulst with associated carrying capacity K. In paper I and II we make the simplifying assumption that a coinfected individual has to, if anything, transmit both of the disease and simply not just one of them. This restriction is relaxed in paper III. In all papers I-III however we do restrict ourselves by letting all transmission rates, that involves scenarios where the newly infected person does not move to same compartment as the infector, to be small. By small we here mean that the results at least hold when the relevant parameters are small enough.In all paper I-III it turns out that for each set of parameters excluding K there exist a unique branch of mostly stable equilibrium points depending continuously on K. We differentiate the equilibrium points of the branch by which compartments are non-zero which we refer to as the type of the equilibrium. The way that the equilibrium point changes its type with K is made clear with the use of transition diagrams together with graphs for the stable susceptible population over K.In paper IV we consider a model for a single age-structured population á la Mckendric-von-Foerster with the addition of differing density dependence on the birth and death rates. Each vital rate is a function of age as well as a weighing of the population also referred to as a size. The birth rate influencing size and the death rate influencing size can be weighted differently allowing us to consider different age-groups to influence the birth and death rate in different proportions compared to other age groups. It is commonly assumed that an increase of population density is detrimental to the survival of each individual. However, for various reasons, it is know that for some species survival is positively correlated with population density when the population is small. This is called the Allee effect and our model includes this scenario.It is shown that the trivial equilibrium, which signifies extinction, is locally stable if the basic reproductive rate $R_0$ is less then 1. This implies global stability with certain extinction if no Allee effect is present. However if the Allee effect is present we show that the population can persist even if R0 < 1.
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| 5. |
- Andersson, Jonathan, et al.
(författare)
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Density-Dependent Feedback in Age-Structured Populations
- 2019
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Ingår i: Journal of Mathematical Sciences. - : Springer Berlin/Heidelberg. - 1072-3374 .- 1573-8795. ; 242:1, s. 2-24
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Tidskriftsartikel (refereegranskat)abstract
- The population size has far-reaching effects on the fitness of the population, that, in its 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 behaviour. In this paper, we develop a rigourous mathematical analysis to study positive and negative effects of increased population density in the classical nonlinear age-structured population model introduced by Gurtin \& MacCamy in the late 1970s. One of our main results expresses the global stability of the system in terms of the newborn function only. We also derive the existence of a threshold population size implying the population extinction, which is well-known in population dynamics as an Allee effect.
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| 6. |
- Andersson, Jonathan, et al.
(författare)
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Effect of density dependence on coinfection dynamics
- 2021
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Ingår i: Analysis and Mathematical Physics. - Basel, Switzerland : Birkhaeuser Science. - 1664-2368 .- 1664-235X. ; 11:4
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Tidskriftsartikel (refereegranskat)abstract
- 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).
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| 7. |
- Andersson, Jonathan, et al.
(författare)
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Effect of density dependence on coinfection dynamics : part 2
- 2021
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Ingår i: Analysis and Mathematical Physics. - : Springer Basel AG. - 1664-2368 .- 1664-235X. ; 11:4
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We consider the remaining parameter values left out from Andersson et al. (Effect of density dependence on coinfection dynamics. arXiv:2008.09987, 2020). We look for coexistence equilibrium points, their stability and dependence on the carrying capacity K. Two sets of parameter value are determined, each giving rise to different scenarios for the equilibrium branch parametrized by K. In both scenarios the branch includes coexistence points implying that both coinfection and single infection of both diseases can exist together in a stable state. There are no simple explicit expression for these equilibrium points and we will require a more delicate analysis of these points with a new bifurcation technique adapted to such epidemic related problems. The first scenario is described by the branch of stable equilibrium points which includes a continuum of coexistence points starting at a bifurcation equilibrium point with zero single infection strain #1 and finishing at another bifurcation point with zero single infection strain #2. In the second scenario the branch also includes a section of coexistence equilibrium points with the same type of starting point but the branch stays inside the positive cone after this. The coexistence equilibrium points are stable at the start of the section. It stays stable as long as the product of K and the rate γ¯γ¯ of coinfection resulting from two single infections is small but, after this it can reach a Hopf bifurcation and periodic orbits will appear.
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| 8. |
- Brommesson, Peter, 1981-
(författare)
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Cattle Shipments and Disease Spread Modeling
- 2022
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Spread of transboundary animal diseases can have large impact on animal welfare, public health and economy. The effects of this include economic losses in terms of lower milk production, lower weight gain and culling due to welfare concerns. Disease preparedness is therefore important to be prepared for a possible outbreak, and policies need to be in place in order to take appropriate actions in case of an outbreak. It is also important to be able to take preventive actions to lessen the risk and size of an outbreak. For this, mathematical models are useful to describe the effects of an outbreak and to facilitate informed policy decisions.Mathematical models of spread of animal diseases, implicitly or explicitly, model the route of infection. One route of particular concern is the shipment of livestock animals since animal shipments have the possibility to move infected animals over long distances and introduce disease in previously unaffected areas. It is therefore important to have underlying data to use as input to models in order to consider possible future scenarios. Such data may however be sparse and not readily available. Based on observed (and sometimes incomplete) data, the underlying process that determines the probabilities of livestock shipments’ origins and destinations can be modeled. By using Bayesian statistics and Markov Chain Monte Carlo methods, it is possible to obtain distributions of the underlying parameters in the model, which in turn allow posterior predictive sets of shipments to be generated. These can further be used in a disease simulation to analyze the course of a potential outbreak. Given a large number of scenarios of interest and substantial stochastic effects, implementation of such models requires fast algorithms to facilitate execution of a sufficient number of replicated simulations, which may be infeasible under naive methods. The topics of this thesis are models of live cattle shipment, the problems of lack of shipment data and the computational challenges of modeling and simulating spread of infectious animal diseases.In Paper I, the spatio-temporal variations in distance dependence of cattle shipments in Sweden were studied by using real shipment data, Bayesian statistics and Markov Chain Monte Carlo methods. The main results were that the spatial as well as the temporal aspect are important when modeling networks of cattle shipments in Sweden. The spatial variations distance dependence were analyzed at county, land (Norrland, Svealand and Götaland) and national level (i.e. no spatial variation). Similarly, the temporal aspect were investigated at three levels of granularity, using monthly-, quarterly- and annual variations (i.e no temporal variation). The level of granularity at which the spatio-temporal variations in distance dependence was captured better, in terms of Deviance Information Criterion, was identified at the county and quarter level. This results shows that such variations should be acknowledged when modeling networks of cattle shipments in Sweden.Paper II considered cattle shipments in the U.S. It addressed the problem of intrastate shipments being absent in available data and included responses from a survey taken by experts to estimate the proportion of shipments moving intrastate. The results showed that data from experts had minor effects on the estimations of proportion of intrastate shipments, mainly because of disparate estimates provided by the experts. This paper also investigated three types of functional forms of the distance dependence, and it was shown that the type used in Paper I, was the least preferred of the three. The preferred functional form had a plateau-shape at short distances as well as a fat tail, describing high probability of long-distance shipments.Paper III addressed the computational challenges of simulating spread of livestock diseases. In Paper III, infections were modeled to spread locally from farm to farm without modeling§ each pathway individually (this may include pathways such as airborne spread, wildlife etc.). To avoid evaluating infection probability of all pairs of infected and susceptible premises, spread of disease was simulated by partitioning the landscape into grids and thereby letting farms belong to a specific cell in this grid. An algorithm was introduced that make use of overestimations of the probability of infection to discard entire cells from further consideration as they are considered as uninfected in the current time frame. Despite introducing estimations of probabilities, the algorithm does not introduce estimations to the spread of disease, and does not compromise the integrity of the simulation. This algorithm was compared to the naive algorithm of evaluating the farms pairwise as well as to two other published algorithms developed for increased computational efficiency. It was shown that the algorithm presented in Paper III was as fast as or faster than other considered methods.Paper IV expanded the methods of Paper II and used the methodology from Paper III to simulate spread of disease via cattle shipments and via local spread across the U.S. In Paper IV, additional data at state- and county level were included that aimed at capturing shipment patterns related to the infrastructure of the production system not captured by the distance dependence. The model also considered three types of premises: farm, feedlot and market. This approach allows for different parameters across premises types, acknowledging their different roles in the production system. The result showed that these types of data were important to include when modeling the system and increased model performance in terms of WAIC, suggesting that industry structure should be accounted for when modeling cattle shipments. The spread of disease simulation included control scenarios such as culling of specific premises and also included a SEIR-model to model the infection status of each premises, referred to as partial transition. The results showed that while the inclusion of partial transition slowed the outbreak, the spatial pattern of the outbreak did not change.This thesis provides insights to what factors are important when predicting animal shipments networks for usage in spread of disease simulations and how these factors can be modeled. It also stresses the importance of efficient algorithms when using simulations and presents an algorithm suited for simulating spread of disease between farms where pathways of the pathogen are not modeled explicitly. How to accurately estimate the spread of disease via shipments and how to simulate a large number of outbreak scenarios within reasonable time are two major challenges a modeler faces when trying to predict the impact of a potential outbreak.
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| 9. |
- Ghersheen, Samia, et al.
(författare)
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Dynamical behaviour of SIR model with coinfection : The case of finite carrying capacity
- 2019
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 42:17, s. 5805-5826
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 10. |
- Ghersheen, Samia, 1985-
(författare)
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Dynamics of Coinfection : Complexity and Implications
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Living beings are always on risk from multiple infectious agents in individual or in groups. Though multiple pathogens' interactions have widely been studied in epidemiology. Despite being well known, the co-existence of these pathogens and their coinfection remained a mystery to be uncovered. Coinfection is one of the important and interesting phenomenon in multiple interactions when two infectious agents coexist at a time in a host. The aim of this thesis is to understand the complete dynamics of coinfection and the role of different factors affecting these interactions.Mathematical modelling is one of the tools to study the coinfection dynamics. Each model has its own limitations and choice of the model depends on the questions to be addressed. There is always a crosstalk between the choice of model and limitation of their solvability. The complexity of the problem defines the restriction in analytical possibilities.In this thesis we formulate and analyse the mathematical models of coinfection with different level of complexities. Since viral infections are a major class of infectious diseases, in the first three papers we formulated a susceptible, infected, recovered (SIR) model for coinfection of the two viral strains in a single host population introducing carrying capacity as limited growth factor in susceptible class. In the first study, we made some assumptions for the transmission of coinfection in the model. In the following papers, the analysis is expanded by relaxing these assumptions which has generated the complexity in dynamics. We showed that the dynamics of stable equilibrium points depends on the fundamental parameters including carrying capacity K. A parameter dependent transition dynamics exists starting from disease free state to a level where coinfection can persists only with susceptible class. A disease-free equilibrium point is stable only when K is small. With increase in carrying capacity to a level where only single infection can invade and persists. Further increase in carrying capacity becomes large enough for the existence and persistence of coinfection due to the high density of susceptible class. In paper I, we proved the existence of a globally stable equilibrium point for any set of parameter values, revealing persistence of disease in a population. This shows a close relationship between the intensity of infection and carrying capacity as a crucial parameter of the population. So there is always a positive correlation between risk of infection and carrying capacity which leads to destabilization of the population.In paper IV, we formulated mathematical models using different assumptions and multiple level of complexities to capture the effect of 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 K. In the first model of this paper, we have also shown the local stability analysis of the boundary equilibrium points and showed that the recovered population is not uniformly bounded with respect to K.Paper V uses simulations to analyse the dynamics and specifically studies how temporal variation in the carrying capacity of the population affects its dynamics. The degree of autocorrelation in variability of carrying capacity influences whether the different classes exhibit temporal variation or not. The fact that the different classes respond differently to the variation depends in itself on whether their equilibrium densities show a dependence on the carrying capacity or not. An important result is that at high autocorrelation, the healthy part of the population is not affected by the external variation and at the same time the infected part of the population exhibits high variation. A transition to lower autocorrelation, more randomness, means that the healthy population varies over time and the size of the infected population decreases in variation.
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