Complex dynamics and optimal treatment of an epidemic model with two infectious diseases

In this paper, we have proposed and formulated an epidemic model with two types of diseasesone is comparative weaker and the other is comparatively stronger with the assumption that both the diseases are active simultaneously in the system. The dynamical behavior of the model; equilibrium analyses with their existence criteria and local stability criteria have been discussed rigorously. With the help of second generation matrix method, we evaluate basic reproduction number of the proposed model. We propose an optimal control problem considering treatment as control parameter and solve it in order to minimize the compound loss due to the presence of infection. All the theoretical results are verified with some appropriate computer simulation works. © Springer Nature India Private Limited 2019.