In this paper, we present a deterministic mathematical model of monkeypox virus by using both classical and fractional-order differential equations. The model includes all of the possible interactions that contribute to disease spread in the population. We investigate the model’s stability results in the disease-free case when R 0 < 1. When R 0 < 1, we show that the model is stable, otherwise it is unstable. To obtain the best fit that describes the dynamics of this disease in Nigeria, the model is fitted using the nonlinear least square method on cumulative reported cases of monkeypox virus from Nigeria between January to December 2019. Furthermore, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We run numerous simulations of the proposed monkeypox model with varied input parameters to investigate the intricate dynamics of monkeypox infection under the effect of various system input parameters. We investigate the system’s dynamical behavior to develop appropriate infection control policies. This allows the public to understand the significance of control parameters in the eradication of monkeypox in the population. Lowering the order of fractional derivatives has resulted in significant modifications. To the community’s policymakers, we offered numerous parameters for the control of monkeypox.

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Summary In this paper, we introduce a dengue disease transmission model with symptomatic and asymptomatic infectious classes. We obtain the threshold dynamics governed by the basic reproduction number of the system. We obtain sensitivity analysis of threshold dynamics to recognize the dominant factors that seriously affect the dengue infection. It has been shown that the biting rate and the rate of asymptomatic cases are more sensitive to the basic reproduction number, and predicts that control of mosquito size plays an essential role in reducing equilibrium level of dengue infection. Hence, the use of mosquito nets and control of population size of mosquitoes are highly suggested to the public. We use optimal control theory to help the public health personnel and biologists to adopt better understanding of the modeling strategies to control dengue fever. We apply preventive control, treatment, and insecticide spray to reach the desire objectives; moreover, the existence of the proposed optimal control problem is established analytically and achieves necessary conditions for optimal controls. The simulations obtained suggested that control measures such as mosquito eradication and preventive strategies effectively eradicate and control dengue infections during the epidemic.

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