# Entropy-based analysis of Rift Valley fever transmission dynamics using delay differential equations

## TL;DR

This paper uses delay differential equations and entropy-based analysis to study the spread of Rift Valley Fever, a dangerous zoonotic disease affecting animals and humans.

## Contribution

The novelty lies in applying entropy-based global stability and delay differential equations to model Rift Valley Fever transmission dynamics.

## Key findings

- The model identifies two equilibria: Rift Valley Fever–Free and Endemic, with stability analyzed using Routh–Hurwitz and LaSalle’s principle.
- Sensitivity analysis highlights key parameters influencing disease transmission and persistence.
- Numerical simulations show how delays affect infection dynamics and susceptibility over time.

## Abstract

Rift Valley Fever (RVF) is a vector-borne, transmissible zoonotic disease in animals and humans caused by RVF virus and transmitted primarily by mosquitoes and biting flies. According to the World Health Organization (WHO), RVF outbreaks have great public health and economic impact, with up to 90% mortality in lambs and approximately 10% in adult sheep. Besides small ruminants, RVF affects cattle, camels, and goats and induces abortion storms and neonatal mortality at high rates, whereas humans develop severe febrile illness, hemorrhagic fever, or encephalitis in extreme cases. In this study, a deterministic epidemic model is developed and studied to investigate the RVF transmission dynamics under inclusion of delay differential equations and an entropy-based global stability approach to capture the time-dependent effect of disease progression. The model separates the ruminant population into susceptible, vaccinated, infected, and recovered, and the mosquito population into susceptible and infected. Positivity, and boundedness are demonstrated as basic dynamical properties. Two equilibria are found and compared: Rift Valley Fever–Free Equilibrium (RVFFE) and Rift Valley Fever Endemic Equilibrium (RVFEE). The basic reproduction number (R0) is derived and local and entropy-based global stability are examined by the Routh–Hurwitz criteria and LaSalle’s invariance principle. Sensitivity analysis reveals the contribution of critical parameters on disease transmission and persistence. Numerical simulations performed using MATLAB’s built-in DDE23 solver assist in revealing the effect of delay on infection dynamics and susceptibility with time. The implications provide tremendous insight into the role of temporal considerations and parameter uncertainty in the transmission dynamics of RVF and enable better understanding as well as potential control strategies for this emerging zoonotic disease.