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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 onchoc

B.G. Jacob, R.J. Novak, L. Toe, M.S. Sanfo, S. Caliskhan, R. Tingueria, A. Pare, M. Noma, L. Yameogo, T.R. Unnasch


In this research,prevalence values based on Monthly Biting Rates (MBR) were employed as aresponse variable in a Poisson probability model framework for quantitativelyregressing multiple georefernced explanatory environmental-related explanatorycovariates of seasonally-sampled larval habitat of Similium damnosum s.l.ablack fly vector of Onchocerciasis  in ariverine study site in Burkina Faso. Results from both a Poisson and then anegative binomial (i.e., a Poisson random variable with a gamma distrustedmean) revealed that the covariates rendered from the model were significant,but furnished virtually no predictive power for mapping endemic transmissionzones. Inclusion of indicator variables denoting the time sequence and thelocational spatial structure was then articulated with Thiessen polygons whichalso failed to reveal meaningful covariates. Thereafter, a spatiotemporalautocorrelation analyses was performed and an Autoregressive Integrated MovingAverage (ARIMA) model was constructed which revealed a prominent first-ordertemporal autoregressive structure in the sampled covariate coefficients. Arandom effects term was then specified which included a specific intercept termthat was a random deviation from the overall intercept term based on a drawfrom a normal frequency distribution. The specification revealed a non-constantmean across the riverine study site. This random intercept represented thecombined effect of all omitted covariates that caused the sampled georeferencedriverine –based villages at the study site to be more prone to onchocerciasisbased on regressed seasonal prevalence rates. Additionally, inclusion of arandom intercept assumed random heterogeneity in the propensity or, underlyingrisk of onchocerciasis which persisted throughout the entire duration of thetime sequence under study. This random effects term displayed serialcorrelation, and conformed closely to a bell-shaped curve. The model’s varianceimplied a substantial variability in the prevalence of onchocerciasis acrossthe study site based on the spatiotemporal-sampled covariates. The modelcontained considerable overdispersion (i.e., excess Poisson variability):quasi-likelihood scale = 69.565. The following equation was then used totranslate and  forecast the expectedclassification 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 + (randomeffect)i]. Seasonally quantitating random effects term estimates, allowingresearch intervention teams to improve the quality of the forecasts for futureonchocerciasis-related predictive autoregressive regression risk-based modelingefforts based on field-sampled S. damnosums.l. explanatory  covariates.


Boatin, B., Molyneux, D.H., Hougard, J.M., Christensen O.W., Alley, E.S., Yaméogo, L., Seketeli, A., Dadzie, K.Y., 1997. Patterns of epidemiology and control of onchocerciasis in West Africa. J. Helminthol., 71 (7), 91–101.

de la Vallée Poussin, C., 1898. Sur les valeurs moyennes de certaines fonctions arithm´etiques, Annales de la soci´et´e sci. Bruxelles., Vol. 22, , 84–90.

Gosper, W., Beeler, M., Gosper, R.W., eds, S., 1972. MIT Artificial Intelligence Laboratory, Memo AIM-239, Cambridge. Massachussetts., pp. 55.

Griffith, D.A., 1897. Spatial autocorrelation and spatial filtering: Gaining understanding through theory and scientific visualization,” Springer-Verlag, Berlin, 2003.N.Nielsen, EenRaekke for Euler’s Konstnat, Nyt.Tidssfor Math., Vol.8B, pp.10-12.

Haight, F.A., 1967. Handbook of the Poisson Distribution, Wiley Press, New York.

Jacob, B.G., Novak R.J., Toe, L., Sanfo, S.M., Afriyne, A.N., Ibrahim, Mohammed G.D.A., Unnasch T.R., 2012. Quasi-likelihood techniques in a logistic regression equation for identifying Simulium damnosum sl. larval habitats intra-cluster covariates in Togo. Geo-spat. Inform. Sci., 15(2), p. 117-133.

McCulloch, C.E., Searle, S.R., 2005. Generalized, Linear and Mixed Models; Wiley-Interscience: New York, NY.

Nielsen, N., 1897. Een Raekke for Euler's Konstant. Nyt. Tidss. for Math., 8B, 10-12.

Sondow, Zudilin, W., 2006. Euler's Constant, -Logarithms, and Formulas of Ramanujan and Gosper, Ramanujan J., Vol. 12, pp. 225-244.

Toe, L., Tang, J., Back, C., Katholi, C.R., Unnasch, T.R., 1997. Vector-Parasite Transmission Complexes for Onchocerciasis in West Africa. Lancet., 349, 163–166.

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