| Abstract: |
| When considering the effects of related diseases in a population, it is useful to create models that incorporate the dynamics of both diseases. However, it is difficult to derive algebraic expressions for the coexistence of multiple diseases in ODE models. We present an ODE model of 2 non-lethal diseases, each without conferred immunity, with coinfection and universal recovery. Our ODE model assumes homogeneous mixing and instantaneous contacts. We calculate the basic reproductive numbers of each disease and of the system as a whole. We explore all possible equilibria, and we determine necessary and sufficient existence criteria and the linear-stability conditions of those that exist under the conditions of our model. We perform both local and global sensitivity analyses of our model. We relax the ODE assumptions of homogeneous mixing and instantaneous contacts by coupling the ODE system with a contact network. The simplest network maintains the homogeneous-mixing assumption, but it involves prolonged lengths of contact. We then increase network complexity, consider bipartite networks and heterogeneous mixing. We perform local and global sensitivity analyses on all ODE and network parameters and discuss how increasing the complexity of the model affects the projected prevalences of the diseases. |
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