Definiability of combinatorial functions and their linear recurrence relationships within a polylogarithmic triangularizable matrix employing surjective bilipschitz functions and other isomorphisms of metric spaces for forecasting seasonal endemic onchocerciasis transmission zones in Burkina Faso

In this research, prevalence values based on Monthly Biting Rates (MBR) were employed as a response variable in a Poisson probability model framework for quantitatively regressing multiple georefernced explanatory environmental-related explanatory covariates of seasonally-sampled larval habitat of Similium damnosum s.l.a black fly vector of Onchocerciasis in a riverine study site in Burkina Faso. Results from both a Poisson and then a negative binomial (i.e., a Poisson random variable with a gamma distrusted mean) revealed that the covariates rendered from the model were significant, but furnished virtually no predictive power for mapping endemic transmission zones. Inclusion of indicator variables denoting the time sequence and the locational spatial structure was then articulated with Thiessen polygons which also failed to reveal meaningful covariates. Thereafter, a spatiotemporal autocorrelation analyses was performed and an Autoregressive Integrated Moving Average (ARIMA) model was constructed which revealed a prominent first-order temporal autoregressive structure in the sampled covariate coefficients. A random effects term was then specified which included a specific intercept term that was a random deviation from the overall intercept term based on a draw from a normal frequency distribution. The specification revealed a non-constant mean across the riverine study site. This random intercept represented the combined effect of all omitted covariates that caused the sampled georeferenced riverine –based villages at the study site to be more prone to onchocerciasis based on regressed seasonal prevalence rates. Additionally, inclusion of a random intercept assumed random heterogeneity in the propensity or, underlying risk of onchocerciasis which persisted throughout the entire duration of the time sequence under study. This random effects term displayed serial correlation, and conformed closely to a bell-shaped curve. The model’s variance implied a substantial variability in the prevalence of onchocerciasis across the study site based on the spatiotemporal-sampled covariates. The model contained considerable overdispersion (i.e., excess Poisson variability): quasi-likelihood scale = 69.565. The following equation was then used to translate and forecast the expected classification value of the prevalence of onchocerciasis into hyperendemic(0-km), (5km to 10 km) mesoendemic,(10-15km) hypoendemic transmission zones at the study site based on the sampled S. damnosum s.l. prevalence rate = exp[-2.9147 + (random effect)i]. Seasonally quantitating random effects term estimates, allowing research intervention teams to improve the quality of the forecasts for future onchocerciasis-related predictive autoregressive regression risk-based modeling efforts based on field-sampled S. damnosums.l. explanatory covariates.

Keywords:

Prevalence , Random effects , Onchocerciasis , Autocorrelation