A fractional order Ebola transmission model for dogs and humans

Abstract

Ebola is a serious disease that affects people; in many cases, it results in death. Ebola outbreaks have also occurred in communities where residents keep pets, particularly dogs. Due to a lack of food, the dogs must hunt for food. Dogs eat the internal organs of wildlife that the locals have killed and eaten, as well as small dead animals that are found within the communities which may contain the Ebola virus. This study introduces a mathematical model based on the Caputo–Fabrizio derivative to describe the Ebola transmission dynamics between dogs and humans. The model’s existence and the uniqueness of its solution were investigated using fixed-point theory. Furthermore, through the Sumudu transform criterion, we established that the Caputo–Fabrizio Ebola model is Picard stable. Some qualitative analysis was also carried out to investigate the Ebola propagation trend in the dog-to-human model. The proposed model is fitted to the reported Ebola incidence in Uganda between October 15, 2022, and November 2, 2022. The Ebola reproduction number obtained using the cumulative data was 2.65. It is noticed that as the fractional order reduces, the Ebola reproduction number also reduces. We derived a numerical scheme for our model using the two-step Lagrange interpolation. It has been discovered that the fractional orders significantly influence the model, indicating that natural occurrences could affect the dynamics of Ebola. It is observed that when the recovery rate is enhanced, such as through the hospitalisation of Ebola-infected individuals, the disease will reduce. Finally, as we ensure a reduction in the contact rate among the dog’s compartments, the disease does not spread adiabatically. Therefore, we urge that quarantine measures be put in place to control interactions among the dogs during the outbreak.