Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Mathematical Modelling for the Transmission Dynamics of blinding Trachoma

Version 1 : Received: 19 May 2021 / Approved: 20 May 2021 / Online: 20 May 2021 (10:57:07 CEST)

How to cite: Muhammad, S.M.; Hincal, E. Mathematical Modelling for the Transmission Dynamics of blinding Trachoma. Preprints 2021, 2021050481. https://doi.org/10.20944/preprints202105.0481.v1 Muhammad, S.M.; Hincal, E. Mathematical Modelling for the Transmission Dynamics of blinding Trachoma. Preprints 2021, 2021050481. https://doi.org/10.20944/preprints202105.0481.v1

## Abstract

Trachsummaroma is an eye infectious disease caused by Chlamydia Trachomatis bacterium, which may lead to irreversible blindness. The disease is spread directly or indirectly by contacting a contaminated material. It can also be transmitted through the disease vector known as “Musca sorbens” or “Bazaar fly”. To curtail the spread of the disease in a population, a meaningful information on the spread and possible control of the disease is required. Mathematical modeling provides efficient tools that can be used to understand and analyze the dynamics of the disease and its control. Several compartmental epidemic models have been proposed in the literature to study the dynamics of trachoma; including SI, SIR and SEIR. However, majority of the existing trachoma models consider only person to person transmission. Thus, the information provided by such models is insufficient since they did not capture the disease vector transmission. The current study proposed a novel SEIR-SEI model that consider both person-person and vector transmission dynamics. The threshold quantity, basic reproduction number R0 is obtained using the next generation matrix, and it was proved that the disease-free equilibrium is asymptotically stable when R0 < 1, and the endemic equilibrium is globally asymptotically stable when R0 > 1. Some simulation results with the aid of mesh plots for the reproductive number as a function of two different biological parameters were obtained. Furthermore, a comprehensive sensitivity analysis is conducted to identify the influence of the individual parameters on the R0. Numerical results show that the vector contact rate has the highest sensitivity with respect to R0, and the value of R0 increases with increase in, hence, the disease can be controlled by decreasing the vector contact rate. Similarly, improving the rate of environmental hygiene and facial cleanliness will decrease the size of R0 and result in the declination of the disease transmission. Moreover, a detailed parameter estimation of the model parameters and model fitting was presented with the use of field data cases from Northern Nigeria using least-square fitting method. The study provides alternative tools that can be used for planning trachoma control program to achieve global eradication of trachoma as a public heath challenge as targeted by WHO in 2030.

## Keywords

Trachoma Model; Reproduction number; Chlamydia Trachomatis; Stability; sensitivity analysis; Model fitting.

## Subject

Computer Science and Mathematics, Computational Mathematics