Cholera, characterized by severe diarrhea and rapid dehydration, is a water-borne infectious disease caused by the bacterium Vibrio cholerae. Haiti offers the most recent example of the tragedy that can befall a country and its people when cholera strikes. While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate and analyze a mathematical model that includes two essential and affordable control measures: water chlorination and education. We calculate the basic reproduction number and determine the global stability of the disease-free equilibrium for the model without chlorination. We use Latin Hypercube Sampling to demonstrate that the model is most sensitive to education. We also derive the minimal effective chlorination period required to control the disease for both fixed and variable chlorination. Numerical simulations suggest that education is more effective than chlorination in decreasing bacteria and the number of cholera cases.

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In this study, a new SIVS epidemic model for human papillomavirus (HPV) is proposed. The global dynamics of the proposed model are analyzed under pulse vaccination for the susceptible unvaccinated females and males. The threshold value for the disease-free periodic solution is obtained using the comparison theory for ordinary differential equations. It is demonstrated that the disease-free periodic solution is globally stable if the reproduction number is less than unity under some defined parameters. Moreover, we found the critical value of the pulse vaccination for susceptible females needed to control the HPV. The uniform persistence of the disease for some parameter values is also analyzed. The numerical simulations conducted agreed with the theoretical findings. It is found out using numerical simulation that the pulse vaccination has a good impact on reducing the disease.

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Recent mathematical modelling has advocated for rapid “test-and-treat” programs for HIV in the developing world, where HIV-positive individuals are identified and immediately begin a course of antiretroviral treatment, regardless of the length of time they have been infected. However, the foundations of this modelling ignored the effects of drug resistance on the epidemic. It also disregarded the heterogeneity of behaviour changes that may occur, as a result of education that some individuals may receive upon testing and treatment. We formulate an HIV/AIDS model to theoretically investigate how testing, educating HIV-positive cases, treatment, and drug resistance affect the HIV epidemic. We consider a variety of circumstances: both when education is included and not included, when testing and treatment are linked or are separate, when education is only partly effective, and when treatment leads to drug resistance. We show that education, if it is properly harnessed, can be a force strong enough to overcome the effects of antiretroviral drug resistance; however, in the absence of education, “test and treat” is likely to make the epidemic worse.