Transmission Dynamics of Two Co-Circulating Strains of Dengue Virus and Effective Vaccination Strategy using Deep Learning

We develop and analyze a deterministic ODE-based model for the transmission dynamics of two cocirculating strains of dengue virus. The model takes into account the interaction between the host and vector populations and also incorporates the effects of partial and temporary cross-immunity and antibody-dependent-enhancement (ADE). The associated basic reproduction numbers for the model are calculated, and it is shown that the disease-free equilibrium is locally asymptotically stable if the maximum of the associated reproduction numbers is less than unity. Our analysis also shows the existence of a backward bifurcation, indicating the possibility of co-existence of a stable endemic equilibrium and a stable disease-free equilibrium even when the basic reproduction number is less than one. The existence and local stability of the partial endemic equilibria are also shown. Numerical exploration of the model shows the existence of oscillatory behavior (limit cycles) under certain parameter regimes. Finally, we examine efficient vaccination protocols by setting up an optimal control problem and using deep neural networks to find the optimal vaccination strategy for a variety of scenarios depending on the model parameters. Besides informing policymakers, this part of the study also demonstrates the potential of machine learning techniques in public health applications.