Modeling control of foot and mouth disease with two time delays

Abstract

We develop a delay ordinary differential equation model that captures the effects of prophylactic vaccination, reactive vaccination, prophylactic treatment and reactive culling on the spread of foot and mouth disease (FMD) with time delays. Simulation results from the study suggest that increasing time delay while increasing the control strategies decreases the burden of FMD. Further, the results reveal, that decreasing time delay while decreasing the control strategies increases the burden of FMD. The intermediate scenarios of either (i) increasing time delay while decreasing control or (ii) decreasing time delay while increasing control have intermediate effects on burden reduction. Thus, the implementation of effective control strategies combination can play an important role in mitigating against the FMD burden.

A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease

“…In recent years, modeling real-world problems using the fractional delay differential equations (FDDEs) has attracted much attention among mathematicians, physicists, and engineers. Due to the wide application of these equations, the theoretical and practical aspects of this category of equations have been extensively studied by researchers in many research articles such as [42,44,49].…”

“…In the light of these facts and after employing the AB-Caputo fractional derivative AB D α and defining two-time delays τ 1 and τ 2 in the model presented in [42], we arrive at the following FDDE for the spread of the disease:…”

“…, A detailed survey of the stability of these equilibrium points can be found in the reference [42].…”

“…In the light of these facts and after employing the AB-Caputo fractional derivative and defining two-time delays and in the model presented in [ 42 ], we arrive at the following FDDE for the spread of the disease: where , and subject to given initial conditions The effective populations in this model are categorized into six state variables as follows: the susceptible subpopulation , the treated and vaccinated subpopulation , the clinically infectious subpopulation , the recovered subpopulation , the vaccinated subpopulation , and finally, the vaccinated carrier subpopulation . We symbolize the sum of all subpopulations by .…”

“…Another interesting study on the disease was conducted to investigate the role of air pollution in the prevalence and incidence of the disease in the warm and cold seasons in Wuhan, China [47]. In [42], the authors investigated some strategies to control the disease using a system of ordinary differential with two delay parameters. To estimate and better understand the transmissibility of HFMD, a susceptible-infected-recovered (SIR) model has been utilized in [26].…”