Ordinary Differential Equation Modeling and a Novel Zubair-Fréchet Distribution for Cholera in Ghana With Control...

In this paper, we present a valuable and novel interdisciplinary study that applies a classic epidemiological model, Susceptible-Infected-Recovered (SIR) to capture the mean disease dynamics, with a novel Zubair Fréchet (ZF) distribution to model the extreme, heavy-tailed nature of cholera outbreak sizes. Furthermore, the proposed model is linked to both public health and actuarial risk. We demonstrate that the ZF provides a superior fit to cholera case data compared to traditional distributions.

Data was collected from both primary sources (such as the Ghana Health Service) and secondary sources. The SIR model employs differential equations in modeling. The results of the simulation study showed that as the sample size was increased, the standard error and bias created by the novel Zubair-Fréchet distribution's parameters decreased while depicting a cholera outbreak. The paper finds that the Zubair-Fréchet distribution is more robust compared to some existing distributions, such as the Fréchet and Weibull distributions. Additionally, a number of actuarial properties were determined, and the maximum likelihood technique was used to estimate model parameters.

Findings from the study show that parameter values of infectious contact rate (beta = 0.004) and recovery rate (gamma = 0.999) make the control strategy effective. ZF fits better than the Fréchet/Weibull distribution, as evidenced from the goodness-of-fit table. Furthermore, vaccination reduces transmission evidenced from the data showing less to no cases after vaccination. The results from this simulation could help guide the Ministry of Health and the Ghana Health Service's response to be able to deploy the necessary logistics, update preparedness, and response plans for the country as the rainy season begins. Industry practitioners may apply this family of distributions to microbiology, public health, and targeted interventions to reduce case fatality rates. Additionally, professionals in the insurance industry can apply our model in insurance value-at-risk and tail value-at-risk for fair premium pricing.