We examine an optimal way of eradicating rabies transmission from dogs into the human population, using preexposure prophylaxis (vaccination) and postexposure prophylaxis (treatment) due to public education. We obtain the disease-free equilibrium, the endemic equilibrium, the stability, and the sensitivity analysis of the optimal control model. Using the Latin hypercube sampling (LHS), the forward-backward sweep scheme and the fourth-order Range-Kutta numerical method predict that the global alliance for rabies control's aim of working to eliminate deaths from canine rabies by 2030 is attainable through mass vaccination of susceptible dogs and continuous use of pre-and postexposure prophylaxis in humans.

No abstract

In this paper, we present and analyze an SEIR Zika epidemic model. Firstly, we investigate the model with constant controls. The steady states of the model is found to be locally and globally asymptotically stable. Thereafter, we incorporate time dependent controls into the model in order to investigate the optimal effects of bednets, treatments of infective and spray of insecticides on the disease spread. Furthermore, we used Pontryagin’s Maximum Principle to determine the necessary conditions for effective control of the disease. Also, the numerical results were presented.

Summary In this paper, we present a co‐infection mathematical model for dengue‐Zika disease in order to carry out their synergistic relationship in the presence of prevention and treatment. Submodel analysis is investigated to establish the reproduction numbers for each disease and to determine the disease‐free local stability equilibrium status. The endemic disease equilibrium is investigated using bifurcation analysis and shows backward bifurcation. We use Pontryagin's maximum principle to explore and determine the best optimal strategies to control both diseases. Numerical optimal control analysis indicates that effective prevention and treatment of each disease will help in the effective control and eradication of the diseases. Finally, the control of co‐infection of dengue‐Zika requires that communities should combine both prevention and treatment associated with each disease at the same time.