Interference of defective particles in the replication of RNA viruses with satellites
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In this project we have investigated a dynamical system describing the dynamics of a standard virus together with its defective interfering particles (DIPs) and a virus satellite. Our model is inspired in the hepatitis B Virus (HBV) - hepatitis Delta Virus (HDV) system, which is currently a major health problem. The HDV is a virus satellite that co-infects with HBV. Double infections with HBV-HDV usually involve a greater impact on patients health. Mathematical models on HBV-HDV systems are scarce in the literature, especially under the impact of the DIPs. DIPs are incomplete virus that typically interfere with the replication of the standard virus (HBV). They have been suggested as possible therapeutic agents decreasing standard viruses fitness. Our model, as far as we know, is the first attempt to describe the dynamics of this 3-virus system, with the standard virus being accompanied by the satellite, together with the DIPs synthesised by the standard virus. We have built a mathematical model based on ordinary nonlinear differential equations, modelling the population dynamics of the three virus types under the processes of competition and interference of DIPs. We have computed the equilibrium points, providing the conditions for the extinction and coexistence of the populations. We have identified transcritical bifurcations involving the transition from a satellite-free scenario i.e., coexistence standard virus-DIPS, to the extinction of the three viral types. Our analytic and numerical results focus on the stability of the system giving place to different scenarios which are relevant from a biomedical point of view.