Background The world's survival ability has been threatened by the COVID-19 outbreak. The possibility of the virus reemerging in the future should not be disregarded, even if it has been confined to certain areas of the world after wreaking such havoc. This is because it is impossible to prove that the virus has been totally eliminated. This research attempts to investigate the spread and control of the COVID-19 virus in Nigeria using the Caputo fractional order derivative in a proposed model. Results We proposed a competent nine-compartment model of Corona virus infection. It starts by demonstrating that the model is epidemiologically sound in terms of solution existence and uniqueness. The basic reproduction threshold R0 was determined using the next-generation matrix technique. We applied the Laplace-Adomian decomposition method to the fractional-order Caputo's derivative model of the Corona virus disease to produce the approximate solution of the model analytically. The obtained results, in the form of an infinite series, were simulated using the MAPLE 18 package to investigate the effect of fractional order derivative on the dynamics of COVID-19 transmission in the model and shed light on methods of eradication. The graphical interpretations of the simulation process were shown and discussed accordingly. Conclusions The study reveals the effect of the Caputo fractional order derivative in the transmission dynamics of the disease. Individual recovery was found to be greatest at an integer order, which represents the full implementation of other factors such as treatment, vaccination, and disease transmission reduction. Hence, we advised that researchers, government officials, and health care workers make use of the findings of this study to provide ways in which disease transmission will be reduced to a minimum to stop the prevalence of COVID-19 by applying the findings of this study.

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Chlamydia disease caused by the Chlamydia trachomatis is one of the major sexually transmitted infectious diseases globally. The progression of this disease has deadly effects cumulating into millions of death. Chlamydia causes numerous complications such as infertility in female, chronic pelvic pain and inflammation. Previous studies did not consider the effects of undetected infected individuals on the dynamic spread of the disease. Hence, this work investigated the effects of undetected infected individuals and efficacy of condom as a contraceptive in the dynamic spread of the disease. A six compartmental model to study the dynamic spread of chlamydia disease was developed using system of ordinary differential equation. The population was divided into susceptible, exposed, infected undetected symptomatic, infected detected symptomatic, infected asymptomatic and recovered individuals. The well-posedness of the model was investigated by the positivity of solution technique. Basic reproduction number (R0) was computed using Next Generation Matrix Method. The endemic equilibrium was investigated by the use of Lyapunov function. The results showed that the disease free equilibrium was stable whenever the basic reproduction number is less than unity (R0<1). The endemic equilibrium was found to be stable as a results of constructed Lyapunov function being negative definite. Numerical analysis showed that increasing in the undetected infected individuals enhanced the spread of the disease. Findings showed that undetected infected individuals played a vital role in the spread of Chlamydia disease. Moreover, using condom as a contraceptive reduced the spread of the disease.