Dynamical analysis of monkeypox transmission incorporating optimal vaccination and treatment with cost-effectiveness

The ongoing monkeypox outbreak that began in the UK has currently spread to every continent. Here, we use ordinary differential equations to build a nine-compartmental mathematical model to examine the dynamics of monkeypox transmission. The basic reproduction number for both humans ( R 0 h) and animals ( R 0 a) is obtained using the next-generation matrix technique. Depending on the values of R 0 h and R 0 a, we discovered that there are three equilibria. The current study also looks at the stability of all equilibria. We discovered that the model experiences transcritical bifurcation at R 0 a = 1 for any value of R 0 h and at R 0 h = 1 for R 0 a < 1. This is the first study that, to the best of our knowledge, has constructed and solved an optimal monkeypox control strategy while taking vaccination and treatment controls into consideration. The infected averted ratio and incremental cost-effectiveness ratio were calculated to evaluate the cost-effectiveness of all viable control methods. Using the sensitivity index technique, the parameters used in the formulation of R 0 h and R 0 a are scaled.