Modeling the Control of Zika Virus Vector Population Using the Sterile Insect Technology

This work is aimed at formulating a mathematical model for the control of mosquito population using sterile insect technology (SIT). SIT is an environmental friendly method, which depends on the release of sterile male mosquitoes that compete with wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring. The basic offspring number of the mosquitoes’ population was computed, after which we investigated the existence of two equilibrium points of the model. When the basic offspring number of the model M0, is less than or equal to 1, a mosquito extinction equilibrium point E2, which is often biologically unattainable, was shown to exits. On the other hand, if M0>1, we have the nonnegative equilibrium point E1 which is shown to be both locally and globally asymptotically stable whenever M0>1. Local sensitivity analysis was then performed to know the parameters that should be targeted by control intervention strategies and result shows that female mating probability to be with the sterile male mosquitoes ρS, mating rate of the sterile mosquito β2, and natural death rates of both aquatic and female mosquitoesμA+μF have greater impacts on the reduction and elimination of mosquitoes from a population. Simulation of the model shows that enough release of sterile male mosquitoes into the population of the wild mosquitoes controls the mosquito population and as such can reduce the spread of mosquito borne disease such as Zika

TRANSMISSION DYNAMICS OF EBOLA VIRUS DISEASE WITH VACCINE, CONDOM USE, QUARANTINE, ISOLATION AND TREATMENT DRUG: Transmission dynamics of Ebola virus disease

Background: Ebola Virus Disease (EVD) has brought the human population, especially the West African race, great losses in so many areas such as economic productivity and human life. During the 2014 Ebola Virus outbreak, the disease devastated and threatened the whole world. EVD symptoms (fever, diarrhea, vomiting, etc) may appear anywhere between two to twenty-one days after infection. Those that recovered from the disease return to being susceptible again and can transmit the virus through semen as research has shown the virus presence in semen even after recovery.   Material and Methods: Mathematical modeling method with the combination of vaccine, condom use, quarantine, isolation and treatment drug together as control measures in a population consisting of human and animals. A model system of non-linear differential equations for the control of EVD was formulated and the model effective reproduction number () was obtained using the next generation matrix method and used in the stability analysis of the model. Center manifold theorem was used in the bifurcation analysis of the model. Results: The result shows that the stability analysis of the model shows that the EVD – Free Equilibrium is locally asymptotically stable when  and EVD - Endemic Equilibrium is locally asymptotically stable when .  The model was shown to exhibit a forward bifurcation. Conclusions: Numerical simulations and analysis of the model show that EVD could be effectively controlled and eradicated within a short period of time when vaccine, condom use, quarantine, isolation and treatment drug control measures are implemented together

Computational Modeling of Trombe Wall Solar Chick Brooding House for Optimal Poultry Production

Computational modeling, simulation and validation were carried out on Trombe wall solar chick brooder used for optimal poultry production. Predictive linear differential equations based on physical, mathematical principles and relationships governing thermo-physical properties of the components of the brooder were formulated, discretized and expressed in their finite different forms using SCILAB 5.5.2. T-test statistics was carried out on predicted and measured mean data: temperature of Trombe wall glaze (TG1), temperature of pebble glaze (TG2), temperature of the pebble bed bin (Tp), temperature of the brooding room (TBr), and temperature of the Trombe wall outer surface (Tw (outer surface))then separated using Levene test for equality. The model adequately predicted the measured temperature of the brooding brooder at 5% probability level

Dynamical System Analysis and Optimal Control Measures of Lassa Fever Disease Model

Lassa fever is an animal-borne acute viral illness caused by the Lassa virus. This disease is endemic in parts of West Africa including Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. We formulate a mathematical model for Lassa fever disease transmission under the assumption of a homogeneously mixed population. We highlighted the basic factors influencing the transmission of Lassa fever and also determined and analyzed the important mathematical features of the model. We extended the model by introducing various control intervention measures, like external protection, isolation, treatment, and rodent control. The extended model was analyzed and compared with the basic model by appropriate qualitative analysis and numerical simulation approach. We invoked the optimal control theory so as to determine how to reduce the spread of the disease with minimum cost