Abstract
Co-infection is a simultaneous multiple parasitic infection within a host, and it is very common in humans and animals. Recently, thanks to molecular tools availability, co-infection has been detected in wild plants and crops. While in humans and animals, co-infection displays higher overall virulence and more severe symptoms, in plants, simultaneous infection can have different outcomes, from lower overall virulence with milder symptoms to higher overall virulence with more severe symptoms driving synergism. In particular, the co-infection driving synergism has threatened several crops. For instance, the co-infection of Beet Yellows Virus (BYV) and Beet Mosaic Virus (BtMV) leads to increased symptoms expression on Sugar Beet. The outbreak in Africa in 2011 of Maize Lethal Necrosis (MLND) as a synergistic interaction between Maize Chlorotic Mottle Virus (MCMV) and potyviruses has threatened the maize yield. Since not allmechanisms driving synergism are currently well known, that makes the study field and control strategies difficult. Mathematical modelling and analysis can help design central strategies or combine strategies to control disease.The aim of this thesis is to use a mathematical framework to develop our understanding of virus interaction driving synergistic co-infection in plants with particular focus on MLND. The mathematical framework follows from the construction of models, their theoretical analysis to the validation through numerical simulations and supplying insight into disease control.The first objective of this thesis is to provide a better understanding of disease dynamics driving synergistic co-infection with particular focus on potyviruses Sugarcane Mozaic Virus (SCMV) and MCMV dynamics driving to MLND and get more insight on disease control of MLND. The second objective is to access the impact of vectors dispersal on co-infection in crop and disease transmission dynamical with special focus on MLND and get more insight on crop protection.To address the first objective of this thesis, we develop a general crop-vector-borne disease temporal deterministic model for synergistic co-infection, with a particular focus on the knowledge we have on the viruses driving the MLND and the vector’s activity. The theoretical analysis of the model shows different thresholds driving the dynamics of the system: the well known basic reproduction number (BRN) and invasion reproduction number (IRN). The latter being essential for the emergence or not of the MLND.To address the second objective of this thesis, we allow vector dispersal by incorporating linear diffusion into the vector population. This model is formulated by partially degenerate reaction-diffusion systems in an unbounded domain. A particular type of solution of interest in this system is the traveling wave solutions. We assess different invasion scenarios depending on the threshold values.Overall, the models developed and analysed in this thesis show, through mathematical modelling, how we can get more understanding of virus interaction driving synergistic co-infection and we also highlight the importance of estimating the BRN and IRN as they summarize the whole dynamics of the system.