We develop a virus-resistant HIV-1 mathematical model with behavioural change in HIV-1 resistant non-progressors. The model hasВ both disease-free and endemic equilibrium points that are proved toВ be locally asymptotically stable depending on the value of the associated reproduction numbers. In both models, a non-linear Goh{Volterra Lyapunov function was used to prove that theВ endemic equilibrium point is globally asymptotically stable for specialВ case while the method of Castillo-Chavez was used to prove the globalВ asymptotic stability of the disease-free equilibrium point. In both theВ analytic and numerical results, this study shows that in the context ofВ resistance to HIV/AIDS, total abstinence can also play an importantВ role in protection against this notorious infectious disease.

Adherence to public health policies such as the non-pharmaceutical interventions implemented against COVID-19 plays a major role in reducing infections and controlling the spread of the diseases. In addition, understanding the transmission dynamics of the disease is also important in order to make and implement efficient public health policies. In this paper, we developed an SEIR-type compartmental model to assess the impact of adherence to COVID-19 non-pharmaceutical interventions and indirect transmission on the dynamics of the disease. Our model considers both direct and indirect transmission routes and stratifies the population into two groups: those that adhere to COVID-19 non-pharmaceutical interventions (NPIs) and those that do not adhere to the NPIs. We compute the control reproduction number and the final epidemic size relation for our model and study the effect of different parameters of the model on these quantities. Our results show that direct transmission has more effect on the reproduction number and final epidemic size, relative to indirect transmission. In addition, we showed that there is a significant benefit in adhering to the COVID-19 NPIs.