A Mathematical Model for Ebola Epidemic With Self-Protection Measures

Abstract

A mathematical model presented in Berge T, Lubuma JM-S, Moremedi GM, Morris N Shava RK, A simple mathematical model for Ebola in Africa, J Biol Dyn 11(1): 42–74 (2016) for the transmission dynamics of Ebola virus is extended to incorporate vaccination and change of behavior for self-protection of susceptible individuals. In the new setting, it is shown that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number [Formula: see text] is less than or equal to unity and unstable when [Formula: see text]. In the latter case, the model system admits at least one endemic equilibrium point, which is locally asymptotically stable. Using the parameters relevant to the transmission dynamics of the Ebola virus disease, we give sensitivity analysis of the model. We show that the number of infectious individuals is much smaller than that obtained in the absence of any intervention. In the case of the mass action formulation with vaccination and education, we establish that the number of infectious individuals decreases as the intervention efforts increase. In the new formulation, apart from supporting the theory, numerical simulations of a nonstandard finite difference scheme that we have constructed suggests that the results on the decrease of the number of infectious individuals is valid.

Modeling the effect of contaminated objects for the transmission dynamics of COVID-19 pandemic with self protection behavior changes

“…We assume that the recovered individuals acquire partial immunity. The released COVID-19 from the exposed and infected individuals through coughing or sneezing landed on materials or surfaces around them and become infected at a rate and , respectively [6] , [19] . The virus decays from the infected surfaces with the decay rate of .…”

“…Behavior change towards using preventive mechanisms by the population to protect themselves from an infectious disease is assumed to be dependent on the way that the disease is transmitted and its fatality [18] . Individuals who have awareness about the disease and decided to use preventive mechanisms have less susceptibility than those without awareness and demonstrating the usual risky behavior [6] , [19] . In this paper, we propose a SEIRDM mathematical model for the transmission dynamics of COVID-19 by introducing a behavior change function.…”

Assessment of effective isolation, safe burial and vaccination optimal controls for an Ebola epidemic model

“…Theorem 5.1 There exists v * ∈ V so that the objective functional in (7) is minimized. Moreover, for small enough T , v * is unique.…”

Dynamical analysis and control strategies in modelling Ebola virus disease

“…Work done by Berge et al [29] was an extension of their previous work done in 2015 [26], in which a simple mathematical model was developed, which incorporated both the direct and the indirect Ebola virus transmission in such a way that there is a provision of Ebola viruses. Models have also been developed to try and understand various intervention strategies in trying to curtail the spread of EVD [31][32][33][34][35][36][37][38][39][40]. The impact of vaccination and vaccines was investigated in [35,36,39,40] and the issue of quarantining analysed in [35,37] through mathematical models.…”

“…Models have also been developed to try and understand various intervention strategies in trying to curtail the spread of EVD [31][32][33][34][35][36][37][38][39][40]. The impact of vaccination and vaccines was investigated in [35,36,39,40] and the issue of quarantining analysed in [35,37] through mathematical models. Further, Berge et al [31] developed a mathematical model to understand the impact of contact tracing as a control strategy of EVD.…”