Page11 FULL LENGTH RESEARCH ARTICLEThe block methods together with their hybrid forms were studied (Onumanyi, et al. 2001) and further investigated Dauda, et al. 2005) and found to be useful for the direct solution of initial and boundary value problems.The advantages of these methods include (i) overcoming the issue of overlap of pieces of solutions usually associated with the multistep finite difference methods and (ii) they are self starting thus eliminating the use of other methods to obtain starting solutions. Before now, the determination of the order of these block methods, their convergence and plotting their absolute stability regions have been done for the single members of the block and whose result may not be assumed for the entire block. In this paper, we consider some of the properties of the entire block. Convergence of the block linear multistep method:In the discreet case, a linear multistep method is said to be convergent if for all initial value problem (1.0) ON SOME PROPERTIES OF THE BLOCK LINEAR MULTI-STEP METHODS*Chollom, J. P.; Ndam, J. N. & Kumleng, G. M. Department of MathematicsUniversity of Jos, Nigeria *(Corresponding author) cholomj@unijos.edu.ng ABSTRACTThe convergence, stability and order of Block linear Multistep methods have been determined in the past based on individual members of the block. In this paper, methods are proposed to examine the properties of the entire block. Some Block Linear Multistep methods have been considered, their convergence, stability and order have been determined using these approaches.
A model describing the dynamics of COVID-19 is formulated and examined. The model is meant to address the impacts of lockdown and social isolation as strategies for the eradication of the pandemic. Local stability analysis indicate that the equilibria are locally-asymptotically stable for R0<1 and R_0>1 for the disease-free equilibrium and the endemic equilibrium respectively. Numerical simulations of the model equations show that lockdown is a more effective strategy in the eradication of the disease than social isolation. However, strict enforcement of both strategies is the most effective means that could end the disease within a shorter period of time.
In this study, a mathematical model of dual latency compartments is developed to investigate the transmission dynamics of COVID-19 epidemic in Oyo state, Nigeria. The model consists of non-pharmaceutical control strategies which include the use of face masks, social-distancing and impact of mass-media on the spread of novel coronavirus in the state. Results indicate control reproduction number \(R_C = 1.4\) with possibilities of high constructive influence of mass-media. Thus, at the fitted values of \(\sigma _f = 0.1,\; \sigma _d = 0.1,\;\sigma _m = 0.6\), the peak of the COVID-19 epidemic is attained after 59,217 infectious quarantined individuals and 328,440 infectious but not quarantined individuals have contracted COVID-19 in about 439 and 443 days respectively from the date of the first incidence. Therefore, efforts on mass-media with programs that can inform the people on effective use of face masks, social-distancing and other safety measures can aid reduction of reproduction number to a value below 1 necessary for eradication of the disease.
A mathematical model for three-species interactions in a food chain, with the assumption that the interacting species are mobile, has been constructed using a combination of Holling's type III and the BD functional responses. Conditions for the onset of diffusive instability were determined. The results indicate the possibility of a stable coexistence of the three interacting species in form of stable oscillations under the reflecting boundary conditions. Habitat segregation also occurs under these conditions. However, under the absorbing boundary conditions, the species experience damped oscillations leading to their extinction. The effects of cross-diffusion of the intermediate and the toppredator were also examined.
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