A six-compartment mathematical model is formulated to investigate the role of media campaigns in Ebola transmission dynamics. The model includes tweets or messages sent by individuals in different compartments. The media campaigns reproduction number is computed and used to discuss the stability of the disease states. The presence of a backward bifurcation as well as a forward bifurcation is shown together with the existence and local stability of the endemic equilibrium. Results show that messages sent through media have a more significant beneficial effect on the reduction of Ebola cases if they are more effective and spaced out.
The role of human behaviour in the dynamics of infectious diseases cannot be underestimated. A clear understanding of how human behaviour influences the spread of infectious diseases is critical in establishing and designing control measures. To study the role that human behaviour plays in Ebola disease dynamics, in this paper, we design an Ebola virus disease model with disease transmission dynamics based on a new exponential nonlinear incidence function. This new incidence function that captures the reduction in disease transmission due to human behaviour innovatively considers the efficacy and the speed of behaviour change. The model’s steady states are determined and suitable Lyapunov functions are built. The proofs of the global stability of equilibrium points are presented. To demonstrate the utility of the model, we fit the model to Ebola virus disease data from Liberia and Sierra Leone. The results which are comparable to existing findings from the outbreak of 2014 − 2016 show a better fit when the efficacy and the speed of behaviour change are higher. A rapid and efficacious behaviour change as a control measure to rapidly control an Ebola virus disease epidemic is advocated. Consequently, this model has implications for the management and control of future Ebola virus disease outbreaks.
The most deadly Ebola outbreak in the history, which started in December [Formula: see text], is currently under control. The high case fatality rate of the Ebola outbreak inspired local and international control strategies. In this paper, the dynamics of Ebola virus disease is modeled in the presence of three control strategies. The model describes the evolution of the disease in the population when educational campaigns, active case-finding and pharmaceutical interventions are implemented as control strategies against the disease. We prove the existence of an optimal control set and analyze the necessary and sufficient conditions, optimality and transversality conditions. We conclude through numerical simulations that containing an Ebola outbreak needs early and long-term implementation of joint control strategies.
MSC Classification: 92B05; 93C15; 92D30; 97M10 During the 2013-2015 Ebola virus disease outbreak, admission into a health facility depended on the availability of hospital beds and health personnel. The limited number of such important logistics contributed to the escalation of the epidemic. We use a compartmental model to study the dynamics of Ebola virus disease when there is a limited number of beds for patients. We use a non-linear hospitalisation rate and formulate the rate at which the time-dependent number of available beds evolves. The model shows a backward bifurcation. Simulation results show that bed supply in Ebola treatment units contribute to the reduction of the number of individuals infected by Ebola virus. The model fitting results suggest that a timely supply of sufficient beds to Ebola treatment units limits the spread of the disease. Despite the fact that bed supplies to Ebola treatment units are not in themselves a control measure, they contribute to the reduction of the disease spread, by keeping the infectious in one place, during their infectious period.These results have important implications to the management and control of the disease.
Migration of infected animals and humans, and mutation are considered as the source of the introduction of new pathogens and strains into a country. In this paper, we formulate a mathematical model of Ebola virus disease dynamics, that describes the introduction of a new strain of ebolavirus, through either mutation or immigration (which can be continuous or impulsive) of infectives. The mathematical analysis of the model shows that when the immigration of infectives is continuous, the new strain invades a country if its invasion reproduction number is greater than one. When the immigration is impulsive, a newly introduced strain is controllable when its reproduction number is less than the ratio of mortality to the population inflow and only locally stable equilibria exist. This ratio is one if the population size is constant. In case of mutation of the resident strain of ebolavirus, the coexistence of the resident and mutated strains is possible if their respective reproduction numbers are greater than one. Results indicate that the competition for the susceptible population is the immediate consequence of the coexistence of two different strains of ebolavirus in a country and this competition is favourable to the most infectious strain. Results also indicate that impulsive immigration of infectives when compared to continuous immigration of infectives gives time for the implementation of control measures. Our model results suggest controlled movements of people between countries that have had Ebola outbreaks despite the fact that closing boundaries is impossible.
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