Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

Abstract

In this study, a mathematical model for studying the dynamics of monkeypox virus transmission with non-pharmaceutical intervention is created, examined, and simulated using real-time data. Positiveness, invariance, and boundedness of the solutions are thus examined as fundamental features of mathematical models. The equilibrium points and the prerequisites for their stability are achieved. The basic reproduction number and thus the virus transmission coefficient ℜ0 were determined and quantitatively used to study the global stability of the model's steady state. Furthermore, this study considered the sensitivity analysis of the parameters according to ℜ0. The most sensitive variables that are important for infection control are determined using the normalized forward sensitivity index. Data from the United Kingdom collected between May and August 2022, which also aid in demonstrating the usefulness and practical application of the model to the spread of the disease in the United Kingdom, were used. In addition, using the Caputo–Fabrizio operator, Krasnoselskii's fixed point theorem has been used to analyze the existence and uniqueness of the solutions to the suggested model. The numerical simulations are presented to assess the system dynamic behavior. More vulnerability was observed when monkeypox virus cases first appeared recently as a result of numerical calculations. We advise the policymakers to consider these elements to control monkeypox transmission. Based on these findings, we hypothesized that another control parameter could be the memory index or fractional order.

Comparative Epidemiological Assessment of Monkeypox Infections on a Global and Continental Scale Using Logistic and Gompertz Mathematical Models

“…In the present study, in addition to addressing different data, scales, and geographical spaces, we aimed to include comparative approaches and novel methodologies. While many epidemiological studies have developed compartmental mathematical models to understand the infectious dynamics of HMPX [ 20 , 21 , 22 , 23 , 46 ], there are not many studies that have attempted to explain the dynamics using a single differential equation for the infected population in HMPX. In this sense, our study provides a primary approximation model for HMPX with two large and well-studied mathematical models, namely the logistic and Gompertz models.…”

“…Infection with the MPXV has previously been modeled using systems of ordinary first-order differential equations [ 20 , 21 ] and fractional order [ 22 , 23 ], which have considered both interaction with a sink for zoonotic transmission (rodents) as well as dissemination among the human population, and in some cases isolation of the sick and vaccination which provides permanent immunity have been also considered. Although models based on systems of differential equations provide a much more detailed explanation of the mechanisms of population propagation and allow us to simultaneously evaluate several epidemiological populations in addition to those infected as susceptible, latent, or recovered, models that characterize a single population, have been shown to fit well with the data in some studies [ 18 , 24 , 25 ].…”

Exploring the dynamics of monkeypox transmission with data-driven methods and a deterministic model

“…Therefore, we carried out a sensitivity analysis of this model parameter concerning the basic reproduction number. The normalized sensitivity index of used in Ngungu et al ( 52 ) and Samuel et al ( 53 ) with respect to parameter is given by When is positive for the parameter , it indicates an increase in , while a negative value of for the parameter suggests a decrease in . Due to complexity of the actual ( Equation 11 ), we consider the normalized sensitivity index ( Equation 14 ) of ( Equation 13 ) with respect to the parameter as follows: …”

A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis

“…Many researchers have worked on numerous ways of reducing the spread of the disease using different modeling approaches, both mathematically and statistically, suggesting ways of mitigating the disease. The modeling of different kinds of viral diseases extended to optimal control and the study of the co-infection of infectious disease dynamics have been the subjects of several studies (see [5][6][7][8][9][10][11][12]). In [2], the authors used a computer algebra system (CAS) simulation procedure to study the model to prevent onchocerciasis using macrofilaricide, which kills the adult worms.…”