Mathematical modelling approach of the study of Ebola virus disease transmission dynamics in a developing country

Background: Ebola Virus causes disease both in human and non-human primatesespecially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date. Materials and Methods:We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus ina population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease-endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle's Invariant principle.Results: The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.Conclusions: Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.

Determining the effects of wind-aided midge movement on the outbreak and coexistence of multiple bluetongue virus serotypes in patchy environments.

Bluetongue virus (BTV) has 27 serotypes with some of them coexisting in different environments which make its control difficult. Wind-aided midge movement is a known mechanism in the spread of BTV. However, its effects on the dynamics of multiple BTV serotypes are not clear. Ordinary differential equation (ODE) and continuous-time Markov chain (CTMC) models for two BTV serotypes in an environment divided into two patches depending on the risk of infection are formulated and analysed. By approximating the CTMC model with a multitype branching process, an estimate for the probability of a major outbreak of two BTV serotypes is obtained. It is shown that without movement a major outbreak occurs in the high-risk patch, but with cattle or midge movement it occurs in both patches. When a major outbreak occurs, numerical simulations of the ODE model illustrate possible coexistence in both patches if the patches are connected by midge or cattle movement. Sensitivity analysis, based on the Latin hypercube sampling method, identified midge mortality and biting rates as being the most important in determining the magnitude of the probability of a major outbreak. These results indicate the significance of wind-aided midge movement on the outbreak and coexistence of multiple BTV serotypes in patchy environments.

Estimating the impact of lock-down, quarantine and sensitization in a COVID-19 outbreak: lessons from the COVID-19 outbreak in China.

In recent history, COVID-19 is one of the worst infectious disease outbreaks currently affecting humanity globally. Using real data on the COVID-19 outbreak from 22 January 2020 to 30 March 2020, we developed a mathematical model to investigate the impact of control measures in reducing the spread of the disease. Analyses of the model were carried out to determine the dynamics. The results of the analyses reveal that, using the data from China, implementing all possible control measures best reduced the rate of secondary infections. However, quarantine (isolation) of infectious individuals is shown to have the most dominant effect. This possibility emphasizes the need for extensive testing due to the possible prevalence of asymptomatic COVID-19 cases.

Consumer-resource coexistence as a means of reducing infectious disease.

Maintaining sustainable ecosystems are important for all the inhabitants of earth. Also, an important component of sustainable ecosystems is the maintenance of healthy coexistence of consumers and their resources which can include diseases in the species involved. We formulate a model, where the resources are plants, to explore how consumer-resource coexistence could of itself limit the spread of infectious diseases. The important mathematical features of the model are discussed using the basic reproduction number and the consumption number. The results show an association between species coexistence and a decrease in ecosystem resource disease. The possible importance of these results are discussed.