Fractional order mathematical model of monkeypox transmission dynamics

Abstract

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.

Monkeypox and the perinatal period: what does maternal–fetal medicine need to know?

“…The researchers analyzed the parameters of the model and found that the human-to-human contact rate was the most sensitive parameter for monkeypox virus transmission. Shortly before, the team presented a deterministic mathematical model using classical and fractional-order differential equations [ 16 ]. Using nonlinear least squares, the researchers fitted new cases of monkeypox in Nigeria from January 2019 to December 2019.…”

Modeling and analysis of monkeypox disease using fractional derivatives

“…There have been few studies on the disease's transmission in the past [ [21] , [22] , [23] , [24] , [25] ]. However, mathematical models have been used to study the transmission of diseases such as COVID-19 [ [34] , [35] , [36] ] and diseases belonging to the family Poxviridae such as smallpox [ [26] , [27] , [28] ], chickenpox [ 29 , 30 ] and cowpox [ 31 ].…”

“…Fractional derivatives have been proposed for application in mathematical models to understand viral infections [ [1] , [2] , [3] , [4] , [5] , [6] , 9 , 11 , 33 ]. Because they have more degrees of freedom than integer-order models, fractional-order models are more precise and trustworthy.…”

“…Veeresha and Prakasha [ 33 ] employed the homotopy analysis transform approach to solve the fractional generalized Zakharov (FGZ) equations using the Atangana-Baleanu fractional derivative model. To investigate the disease's spread in Nigeria, Peter et al [ 11 ], developed both traditional and Caputo-Fabrizio fractional-order derivative models. This is the only fractional-order derivative model of the monkeypox virus.…”

The impact of COVID-19 on a Malaria dominated region: A mathematical analysis and simulations

“…For many decades, mathematical models have been formulated and examined to study how various epidemic diseases are controlled and spread. For example, see [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] and the references therein. To better understand the dynamics of co-infection diseases, some studies have been developed (see [21] , [35] , [36] , [4] , [37] ).…”