The Effect of Delay Techniques on a Lassa Fever Epidemic Model

Abstract

The delayed intervention techniques in real-world problem modelling have a significant role in behavioural, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Delayed modelling of real-world problems is a powerful tool and nonpharmaceutical technique for understanding the dynamics of disease in a population. This paper considers real-world problems like the Lassa fever model. According to the World Health Organization (WHO), Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, Togo, Nigeria, and West Africa are the most affected countries with Lassa fever. The most dangerous situation is that eighty percent of the infected persons have no symptoms. To study the dynamics of Lassa fever, two types of populations are considered humans and rats. The human population includes susceptible, infected, and recovered. The rat population includes susceptible and infectious rodents. By introducing a delay parameter and decay exponential term into the existing model in the literature, we got the system of highly nonlinear delay differential equations (DDEs). The fundamental properties such as positivity, boundedness, existence, and uniqueness are verified for the said model. The equilibrium and reproduction number of the model are discussed. The reproduction number for the Lassa fever model is analyzed using the next-generation matrix method. If the reproduction number is less than one, this situation helps eradicate the disease. If the reproduction number is more significant than one, then the virus will spread rapidly in human beings. We have also investigated the effect of the delay factor on reproduction numbers. The local and global stabilities for both equilibria of the model have also been presented. Furthermore, computer simulations are designed to analyze the academic behaviour of the model.