In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies α and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort α was found to be the most sensitive parameter in the reduction of ℛ 0 . Hence, numerical simulations were performed using different values of α to determine an optimal value of α that reduces the incidence rate fastest. It was discovered that an optimal combination that reduces the incidence rate fastest comes from about 40 % of adherence to the preventive strategies coupled with about 40 % of infected humans seeking clinical treatment, as this will reduce the infected human and vector populations considerably.

The continual wearing of road surfaces results to crack and holes called potholes. These road surface irregularities often elongate travel time. In this paper, a second-order macroscopic traffic model is therefore proposed to account for these road surface irregularities that affect the smooth flow of vehicular traffic. Though potholes do vary in shape and size, for simplicity the paper assumes that all potholes have conic resemblances. The impact of different sized potholes on driving is experimented using fundamental diagrams. Besides, the width of these holes, driver reaction time amid these irregularities also determine the intensity of the flow rate and vehicular speed. Moreover, a local cluster analysis is performed to determine the effect of a small disturbance on flow. The results revealed that the magnitude of amplification on a road surface with larger cracks is not as severe as roads with smaller size holes, except at minimal and jam density where all amplifications quickly fade out.

In this paper, we prove that the Wronskian W (λ) of the boundary condition functions for the following boundary value problem π:a) = φ / (a) = φ (b) = φ / (b) = 0 is asymptotically equivalent for large values of |λ|, to the Wronskian of the boundary condition functions of the corresponding Fourier problem π F given by π F : φ (4) (x) = λφ (x) , φ (a) = φ / (a) = φ (b) = φ / (b) = 0.

Many diseases like cystic fibrosis and sickle cell anemia disease (SCD), among others, arise from single point mutations in the respective proteins. How a single point mutation might lead to a global devastating consequence on a protein remains an intellectual mystery. SCD is a genetic blood-related disorder resulting from mutations in the beta chain of the human hemoglobin protein (simply, β-globin), subsequently affecting the entire human body. Higher mortality and morbidity rates have been reported for patients with SCD, especially in sub-Saharan Africa. Clinical management of SCD often requires specialized interdisciplinary clinicians. SCD presents a major global burden, hence an improved understanding of how single point mutations in β-globin results in different phenotypes of SCD might offer insight into protein engineering, with potential therapeutic intervention in view. By use of mathematical modeling, we built a hierarchical (nested) graph-theoretic model for the β-globin. Subsequently, we quantified the network of interacting amino acid residues, representing them as molecular system of three distinct stages (levels) of interactions. Using our nested graph model, we studied the effect of virtual single point mutations in β-globin that results in varying phenotypes of SCD, visualized by unsupervised machine learning algorithm, the dendrogram.

In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies (α) and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort α, was found to be the most sensitive parameter in the reduction of R0. Hence, numerical simulations were performed using different values of α to determine an optimal value of α that reduces the incidence rate fastest.It was discovered that an optimal combination that reduces the incidence rate fastest comes from about 40% of adherence to the preventive strategies coupled with about 40% of infected humans seeking clinical treatment as this will reduce the infected human and vector populations considerably.