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Register a new userEffect of density dependence on coinfection dynamics
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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.
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In this paper we continue the stability analysis of the model for coinfection with density dependent susceptible population introduced in the 1st part of the paper. 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 section of coexistence points starting at a bifurcation equilibrium point with zero second single infections and finishing at another bifurcation point with zero first single infections. 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 $bar gamma$ 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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We prove that the Sierpinski curve admits a homeomorphism with strong mixing properties. We also prove that the constructed example does not have Bowens specification property.
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