Mathematical Modelling and Transmission on the Dynamic of Syphilis with Exposed, Early and Late Latent Syphilis

Authors

  • Ali Inalegwu Michael Federal University Wukari, Nigeria
  • Washachi Dekera Jacob Nigerian Army University Biu, Nigeria

DOI:

https://doi.org/10.57233/ijsgs.v10i1.609

Keywords:

Syphilis, Risky Sexual Behaviour, Prevalence, Global Stability, Incubation period.

Abstract

This research presents a Mathematical Modelling and Transmission on the Dynamic of Syphilis with Exposed, Early and Late Latent Syphilis. The model is governed by a system of six ordinary differential equations namely: Susceptible (S), Exposed (E), Early latent, Late latent Infected  and Recovery (????).  An analysis was performed on the model to determine the disease-free equilibrium, endemic equilibrium, reproduction number, local stability, and global stability. The results of the analysis indicate that the disease-free equilibrium equation is locally asymptotically stable if the reproduction number is less than one, and unstable if the reproduction number is greater than one.  The system has met all the requirements to be considered globally asymptotically stable. We have conducted numerical simulations of the model, and the results show that the number of people who are exposed will keep increasing. It will only decrease if people become aware of the syphilis problem in the community. If a person is mildly infected with a virus but shows no symptoms, they can still spread the virus and cause harm. However, if the infected person gets treated during the latency period, which is the time between infection and onset of symptoms, they can recover within the first five weeks of the pandemic. This information is supported by a graph. In general, the number of syphilis cases will decline over time if they are properly treated. On the other hand, if left untreated, out of every 300 individuals, 280 will be affected by syphilis. However, those who have recovered from syphilis suggest that with appropriate care, treatment, and safe sexual behaviour, it is possible to avoid contracting syphilis.

Author Biographies

Ali Inalegwu Michael, Federal University Wukari, Nigeria

Department of Mathematics and Statistics Federal University Wukari, Nigeria

Washachi Dekera Jacob, Nigerian Army University Biu, Nigeria

Department of Mathematics Nigerian Army University Biu, Nigeria

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Published

2024-03-31

How to Cite

Michael, A. I. ., & Washachi , D. J. (2024). Mathematical Modelling and Transmission on the Dynamic of Syphilis with Exposed, Early and Late Latent Syphilis. International Journal of Science for Global Sustainability, 10(1), 175–184. https://doi.org/10.57233/ijsgs.v10i1.609