Dynamical analysis and control strategies in modelling Ebola virus disease

Abstract

Ebola virus disease (EVD) is a severe infection with an extremely high fatality rate spread through direct and indirect contacts. Recently, an outbreak of EVD in West Africa brought public attention to this deadly disease. We study the spread of EVD through a two-patch model. We determine the basic reproduction number, the disease-free equilibrium, two boundary equilibria and the endemic equilibrium when the disease persists in the two sub-populations for specific conditions. Further, we introduce time-dependent controls into our proposed model. We analyse the optimal control problem where the control system is a mathematical model for EVD that incorporates educational campaigns. The control functions represent educational campaigns in their respective patches, with one patch having more effective controls than the other. We aim to study how these control measures would be implemented for a certain time period, in order to reduce or eliminate EVD in the respective communities, while minimising the intervention implementation costs. Numerical simulations results are provided to illustrate the dynamics of the disease in the presence of controls.

Analysis of seir model with a single control for COVID-19

“…Figure (4) shows that the Figure 3: Flow of Variables with respect to Time without vaccination susceptible with vaccination is less than without vaccination, which shows that vaccination can decrease the spread of the disease. On the study of variable of exposed figure (5) shows that the Exposed with vaccination is reduced from day 1 and without vaccination is higher.…”

“…Moussa Barro [7] has introduced an optimal control for a SIR model with time delay. A. Mhlannga [5] formulated and analyzed the two patch model for Ebola virus disease.…”

A novel control set-valued approach with application to epidemic models

“…Assume that ξ and G(•) are continuous on D, then any continuous selection of the feedback map G provides a control law that leads to a viable solution to system (10) in D. This is so for minimal selection whenever it is continuous. Otherwise we may use [28,Theorem 4.3.2] as follows:…”

“…The authors used two control variables which represent the effectiveness rates of vaccination and travel-blocking operation, and they focus to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Another work that concerns the control of the Ebola virus disease was proposed by Mhlanga [10]. The mathematical model includes control functions representing educational campaigns in their respective patches, with one patch having more effective controls than the other.…”

Assessing the Impact of Optimal Health Education Programs on the Control of Zoonotic Diseases

“…Furthermore, a stronger result regarding the global dynamics of the DFE can be established. We will utilize the approach of Lyapunov functions [27][28][29][30][31] in the analysis of global asymptotic stability.…”