Articles: Department of Mathematics and Statistics

Permanent URI for this collection

http://repository.embuni.ac.ke/handle/123456789/611

Browse

Browsing Articles: Department of Mathematics and Statistics by Subject "Basic reproduction number"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    A Deterministic Model Of HIV Transmission Between Two Closed Patches Incorporating The Monod Equation
    (IISTE, 2019-11-06) Ngari, Cyrus, G; Mirgichan, James, K; Karanja, Stephen
    Among other factors, migration has significantly contributed to the spread of HIV. Recent studies have revealed that new infections occur along major transport corridors and truck-drivers have overall higher prevalence rates of HIV and sexually transmitted infections than non-truck drivers’ counterparts. Therefore, there exist a link between population mobility and HIV infection, as populations along transport corridors remain substantial contributors of new infections. This research work documents a deterministic model of the dynamics of HIV transmission between two closed patches that incorporates the Monod equation in migration with truck drivers being the agents of HIV transmission. Migration is considered as a social determinant to health and have a significant impact on health‐ related vulnerabilities and access to services. We assumed that susceptible individuals become infected via sexual intercourse with HIV infected truck drivers and all the infected individuals ultimately developed AIDS exponentially. The model also assumed that the patches have different infection and susceptibility rates. The patches basic reproduction number, 𝑅0 was determined using the Next Generation Matrix. The results revealed that 𝑅0 should be kept below unity to eradicate the transmission of the virus. The Disease-Free Equilibrium Point was obtained based on the signs of the Eigen values of the Jacobian matrix. In the absence, the Disease-Free Equilibrium Point is both Locally Asymptotically and Globally Asymptotically Stable. It was further proved that the model did not display Endemic Equilibrium Point under a special property for epidemic models. The model findings are vital in guiding health practitioners, governmental and non-governmental health agencies in the development of effective mitigation strategies to reduce the spread of HIV.
  • Thumbnail Image
    Item
    A model for childhood Pneumonia Dynamics
    (Asian online journals, 2014) Ngari, Cyrus G.; Malonza, David M.; Muthuri, Grace G.
    This paper presents a deterministic model for pneumonia transmission and uses the model to assess the potential impact of therapy. The model is based on the Susceptible-Infected-Treatment-Susceptible compartmental structure with the possibility of infected individual recovering from natural immunity. Important epidemiological thresholds such as the basic and control reproduction numbers ( 𝑅𝑜and 𝑅𝑐 respectively) and a measure of treatment impact are derived. Infection free point was found to be locally stable but globally unstable. We found that if the control reproduction number is greater than unity, then there is a unique endemic equilibrium point and it is less than unity, the endemic equilibrium point is globally asymptotically stable, and pneumonia will be eliminated. Numerical simulations using Matlab software suggest that, besides the parameters that determine the basic reproduction number, natural immunity plays an important role in pneumonia transmissions and magnitude of the public health impact of therapy. Further, treatment regimens with better efficacy holds great promise for lowering the public health burden of pneumonia disease.
  • Thumbnail Image
    Item
    Tuberculosis model, a case study of tigania west, Kenya
    (2016) Muthuri, Grace G.; Malonza, David; Ngari, Cyrus G.
    Tuberculosis (TB) is a bacterial disease caused by mycobacterium tuberculosis. Many mathematical models for TB have been developed but not specifically for Kenya. This study develops a deterministic model based on Susceptible–Exposed–Active–Treated compartments classes. The model analyses the stability of the disease free equilibrium by analyzing the basic (R0) and control (RC) reproduction number and the endemic equilibrium point (EEP) which shows that the model is stable when RC< 1 and there exist an EEP when RC is less than one. Sensitivity analysis of the model was investigated using the partial derivatives of (RC) with respect to treatment which shows that high rate of treatment reduces the control reproduction number so is the best intervention method in Kenya.