ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 9 (2013) No. 4, pp. 302-320 ‘Transmission dynamics of trichomoniasis in bisexuals’ without the ‘E’ Phillip Mafuta, Josiah Mushanyu, Steady Mushayabasa, Claver P. Bhunu * Department of Mathematics, Box MP 167, Mount Pleasant, Harare, Zimbabwe (Received January 10 2013, Revised June 11 2013, Accepted September 22 2013) Abstract. A deterministic model for transmission dynamics of Trichomonas vaginalis in a population with bisexuals is formulated and analysed. The disease free equilibrium point has been shown to be globally asymptotically stable when the reproduction number is less than a unity. Furthermore, the endemic equilib- rium point has been shown to be locally asymptotically stable and globally asymptotically stable for when the reproduction number is greater than a unity, using the Centre manifold theory and Liapunovs functional approach, respectively. Analysis of the reproduction number has shown that an increase in the number of infected bisexuals result in an increase in the number of infectives among heterosexuals and vise-versa. This suggests that straight women are turning into bisexuals already infected and that bisexuals are linked to straight females indirectly by males. Simulations results has shown that treatment is the major parameter in controlling the spread of the infection. Keywords: reproduction number, bisexuality, treatment. 1 Introduction Trichomoniasis is abbreviated as TV, it is a sexually transmitted Infection (STI) or a sexually transmit- ted disease (STD) [10] . A single celled protozoan (microscopic parasite) called trichomonas vaginalis is the causative agent, usually this parasite is found in the vagina and urethral tissues [4, 5, 10, 14] . Trichomoniasis is diagnosed by visually observing the trichomonands via a microscope, this is so, because, trichomonands are too small to be seen by a naked eye [6, 10, 17] . The trichomonands are pear shaped and have several flagella (whip-like tails) at one end. In women, TV is detected through inserting a speculum into the vagina, followed by collecting a sample of vaginal discharge using a cotton-tipped applicator. The collected sample will then be placed onto a microscopic slide and sent to a laboratory to be analyzed. Results on TV tests may also reveal small red ulcerations on the vaginal wall or cervix [9] . It is a far more sexually transmitted infection than either Clamydia trachomatis or Neisseria gonorrhoea [2, 19] . Some researchers have shown that trichomoniasis is more prevalent in females (67-100 percent of fe- male sexual partners of an infected male get infected) than males (14-60 percent of male sexual partners of an infected female get infected) [2, 10, 11, 19] . The reason why females are more infected is poorly understood, although some researchers have the idea that the pro-static fluid contains zinc and other substances that are harmful to the pathogen [2, 21, 22] . The WHO has estimated that 160 million cases of infection are acquired an- nually worldwide [3] . The estimates for North America alone are between five and eight million new infections each year, with estimated rate of asymptomatic cases as high as fifty percent [3–5, 23] . Some researchers have also shown that trichomonas vaginalis is more prevalent in industrialised countries [2, 6, 12] . In females, the parasite usually affects the vagina, urethra, cervix, bladder and glands in genital areas [15, 17, 18] . In males, the parasite infects the urethra or under the foreskin of the penis if it is not cir- cumcised. Females usually reveal symptoms, while infection in males are usually asymptomatic. Signs and * Corresponding author. E-mail address: cpbhunu@gmail.com. Published by World Academic Press, World Academic Union