In this study, the spread of the monkeypox virus is investigated through the dynamical study of a novel Caputo fractional order monkeypox epidemic model. The interaction between human and rodent populations along with the effects of control signals are considered in the model. These control signals are established through the optimal control strategy. Furthermore, the effect of memory is examined via varying fractional order parameters in the model. The influences of other parameters are also examined. The positivity and boundness of the solution are verified through theoretical analysis. In addition, the equilibrium points for the system are obtained for both the free and endemic cases, and the local stability has been studied. To verify the theoretical findings, numerical experiments are conducted. The optimal control signals are obtained and verified through numerical simulations of different configurations of control parameters. From these simulations, it is found that the optimal control scheme can help in reducing the size of the infected, quarantined, and exposed categories while increasing the susceptible and recovered categories. These acquired results can provide some assistance to governments in providing some preventive control to suppress the spread of the virus.

This paper is devoted to the model of Lassa hemorrhagic fever (LHF) disease in pregnant women. This disease is a biocidal fever and epidemic. LHF disease in pregnant women has negative impacts that were initially appeared in Africa. In the present study, we find an approximate solution to the fractional-order model that describes the fatal LHF disease. Laplace transforms coupled with the Adomian decomposition method (ADM) are applied. In addition, the fractional-order LHF model is numerically simulated in terms of a varied fractional order. Furthermore, a fractional order optimal control for the LHF model is studied.