Abstract
BackgroundThough different forms of control measures have been deployed to curtail disease transmission, which are mostly through vaccination, treatment, isolation, etc., using mathematical models. Therefore, there is a need to consider the strict compliance or attendance of human individuals to medical awareness program through media outlets like radio, television, etc. In this work, a generalized mathematical model of two groups of infectious individuals who are compliant and non-compliant to medical awareness program is studied.ResultsA generalized Susceptible-Exposed-Infected-Recovered (SEIR) model with two groups of infectious individuals who attend or are compliant and those who do not attend or are non-compliant to medical awareness program is established. The analytical results of the model shows that the model is positive, well-posed, and epidemiologically reasonable. The two equilibria and the basic reproduction number Rr of the model is computed and analyzed and it is shown that the disease-free equilibrium is locally and globally asymptotically stable when Rr < 1 and the endemic equilibrium is globally stable when Rr > 1. Simulations are carried out by varying some parameters when Rr is less and above unity. The simulations suggest that control interventions are to be implemented and medical awareness program scaled up to mitigate the spread of diseases. Furthermore, two numerical methods of Runge-Kutta and Differential Transform Method (DTM) are employed to obtain the approximate solutions of the model system equations, and it is observed that the results of the two methods agreeably compare with each other in terms of efficiency and convergence.ConclusionThis work should be taken into consideration by health policy makers and bio-mathematicians, because existing literature only take into consideration, how diseases spread and its management without considering the impact of strict compliance to consistent awareness program to mitigate the spread of diseases, which has been considered in this work. The limitation of this work is the unavailability of data on individuals in disease endemic regions who always and who do not comply with medical awareness programs.
Highlights
ResultsA generalized Susceptible-Exposed-Infected-Recovered (SEIR) model with two groups of infectious individuals who attend or are compliant and those who do not attend or are non-compliant to medical awareness program is established
Though different forms of control measures have been deployed to curtail disease transmission, which are mostly through vaccination, treatment, isolation, etc., using mathematical models
The basic reproduction number Rr is an epidemic threshold used to determine the number of secondary cases of infections arising as a result of an introduction of an infected individual into a susceptible host population during his or her period of infection
Summary
A generalized Susceptible-Exposed-Infected-Recovered (SEIR) model with two groups of infectious individuals who attend or are compliant and those who do not attend or are non-compliant to medical awareness program is established. The analytical results of the model shows that the model is positive, well-posed, and epidemiologically reasonable. Simulations are carried out by varying some parameters when Rr is less and above unity. The simulations suggest that control interventions are to be implemented and medical awareness program scaled up to mitigate the spread of diseases. Two numerical methods of Runge-Kutta and Differential Transform Method (DTM) are employed to obtain the approximate solutions of the model system equations, and it is observed that the results of the two methods agreeably compare with each other in terms of efficiency and convergence
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