Parameter-dependent transmission dynamics and optimal control of foot and mouth disease in a contaminated environment

Francis Mugabi,Joseph Mugisha,Betty Nannyonga,Henry Kasumba,Margaret Tusiime

doi:10.1186/s42787-019-0058-1

Francis Mugabi, Joseph Mugisha + Show 3 more

Open Access

https://doi.org/10.1186/s42787-019-0058-1

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Abstract

The problem of foot and mouth disease (FMD) is of serious concern to the livestock sector in most nations, especially in developing countries. This paper presents the formulation and analysis of a deterministic model for the transmission dynamics of FMD through a contaminated environment. It is shown that the key parameters that drive the transmission of FMD in a contaminated environment are the shedding, transmission, and decay rates of the virus. Using numerical results, it is depicted that the host-to-host route is more severe than the environmental-to-host route. The model is then transformed into an optimal control problem. Using the Pontryagin’s Maximum Principle, the optimality system is determined. Utilizing a gradient type algorithm with projection, the optimality system is solved for three control strategies: optimal use of vaccination, environmental decontamination, and a combination of vaccination and environmental decontamination. Results show that a combination of vaccination and environmental decontamination is the most optimal strategy. These results indicate that if vaccination and environmental decontamination are used optimally during an outbreak, then FMD transmission can be controlled. Future studies focusing on the control measures for the transmission of FMD in a contaminated environment should aim at reducing the transmission and the shedding rates, while increasing the decay rate.

Highlights

Foot and mouth disease (FMD) is a highly contagious viral disease that affects all clovenhoofed domestic and wild animals [3]
The model is shown to have a locally and globally asymptotically stable disease-free equilibrium point whenever its associated reproduction number is less than unity and has a unique, locally asymptotically stable endemic equilibrium point when R0 exceeds unity
The existence of a stable disease-free equilibrium point implies that the classical requirement of having the basic reproduction number less than unity is necessary and sufficient for the control of the transmission of FMD in a contaminated environment

Summary

Introduction

Foot and mouth disease (FMD) is a highly contagious viral disease that affects all clovenhoofed domestic and wild animals [3]. FMD is caused by a virus of genus Aphthovirus of the family Picornaviridae [8]. The mortality rate of animals due to FMD is usually low but may be high depending on the age of the animals. The control measures against FMD include vaccination, quarantine, bio-security measures, and killing the infected animals [7]. FMD can be transmitted either directly through contact with an infected host [4] or indirectly through contact with a contaminated environment [9]. Direct transmission of FMD occurs when infected and susceptible animals get in close contact with each other

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