Predator-prey models describe the interaction between two species, the prey which serves as a food source to the predator. The migration of the prey for safety reasons after a predator attack and the predator in search of food, from a patch to another may not be instantaneous. In this paper, a Rosenzweig-MacAurther model with a Holling-type II predator functional response and time delay in the migration of both species is developed and analysed. Stability analysis of the system shows that depending on the prey growth and prey migration rates either both species go to extinction or co-exist. Numerical simulations show that a longer delay in the migration of the species leads makes the model to stabilize at a slower rate compared to when the delay is shorter. Relevant agencies likethe Kenya Wildlife Service should address factors that slow down migration of species, for example, destruction of natural habitats for human settlement and activities, which may cause delay in migration.

Diarrhoeal diseases are the major cause of child mortality in developing countries, where access to clean drinking water and sanitation is a problem. In this paper, we develop and analyse a mathematical model for cholera transmission incorporating media coverage. The existence and stability of the equilibrium points is established. Analysis of the model shows that the disease free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity while the endemic equilibrium is locally asymptotically stable when the reproduction number is greater than unity. Numerical simulations done using the MATLAB software indicate that when media coverage is very efficient, the number of cholera infectives decreases faster, impliying that media alert and awareness campaigns are vital in controlling the spread of cholera.

Despite the preventive and control strategies in place, ZikV disease still persists especially in the Western countries and the Pacific islands. In this study, a spatiotemporal model is developed and analyzed to describe the transmission dynamics of ZikV disease and deduce potential control strategies. Positivity and boundedness of solutions of the model with zero flux boundary conditions are shown. The basic reproduction number, R0, is computed using the next generation matrix approach. Model analysis shows that the disease-free equilibrium (DFE) point is both locally and globally asymptotically stable provided that R0 < 1, which implies that the disease would not invade the population under study. The endemic equilibrium (EE) is locally

Predator-prey models describe the dynamics of ecological systems in which two species, the predator and the prey, interact. The objective of this study is to formulate and analyze a predator-prey mathematical model, based on a system of delay differential equations that takes into consideration time delay in migration, with a prey migration rate that depends on the predator density and other factors like availability of its food. It is shown that the population density mainly depends on both barriers during migration and the migration rate. The rates of migration may be affected by factors such as infrastructure through natural habitat, destruction of the natural habitat through logging, natural disasters like re-outbreaks among others. In view of this, relevant agencies should employ measures which will deal with factors which slow down the rate of migration or cause barriers during migration for example reducing natural habitat land allocation to human settlement, agriculture or infrastructure.

Current treatment for HIV infection consists of Highly Active Antiretroviral (ART) therapy. However, lack of adherence to ART treatment has hampered the benefits of the ART treatment strategy and viral load suppression. Most of the treatment models studied so far do not explicitly include the relationship between adherence to ART regimens and viral load suppression. In this study, a mathematical model with ART adherence is developed. By an application of the next generation matrix approach, the reproduction number, R0, is determined.Stability analysis of the model developed shows that the Disease Free Equilibrium (DFE) is locally asymptotically stable, if R0 < 1, and an Endemic Equilibrium (EE) exists, which is unique and is locally asymptotically stable when R0 > 1. Using Lyapunov functional approach, the endemic equilibrium is shown to be globally asymptotically stable, and hence persistence of the disease in the population.