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Using calculus to slow the spread of infectious disease

JAN 12, 2024
Fractional calculus model provides insight into the efficacy of various control factors to advise public health officials in controlling the spread of the mpox infection.
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Mpox, formerly known as monkeypox, is an infectious viral disease that can spread from animals and between people. Though rarely fatal, mpox causes uncomfortable blisters, sores, and fever. The virus is endemic in parts of Africa, but after a global outbreak in 2022, the WHO declared it a public health emergency.

Biswas et al. employed a fractional calculus framework to model mpox transmission and how various intervention strategies can reduce spread.

“Our aim was to investigate the effectiveness of a range of strategies in controlling the spread of the infection, which will help in refining the existing policies, developing novel, evidence-based approaches for enhancing the control of disease spread, and ultimately safeguarding public health and well-being,” said author Humaira Aslam.

Their model includes rodent mpox carriers, aware and unaware humans, vaccinated and unvaccinated, as well as the aftermath of contracting the disease. They introduced various control strategies to examine which are the most effective.

“An important parameter is the effective treatment of symptomatic individuals,” said Aslam. “This parameter has a negative sensitivity index, which implies that increasing the treatment rate of symptomatic infected humans would lead to a decline in the basic reproduction number, indicating it as a scientifically sound and effective control strategy for curbing the spread of the infection.”

Other control strategies like raising awareness, reducing contact with those infected, and increasing vaccination rate are also beneficial to limit mpox spread.

This fractional calculus model can be modified to investigate other transmissible diseases, but the authors plan to focus on the optimal control policy to limit mpox transmission.

Source: “Mathematical modelling of a novel fractional-order monkeypox model using Atangana-Baleanu derivative,” by A. Santanu Biswas, B. Humaira Aslam, and Pankaj Kumar Tiwari, Physics of Fluids (2023). The article can be accessed at https://doi.org/10.1063/5.0174767 .

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