International Journal of Mathematical Modelling and Numerical Optimisation (8 papers in press)

Regular Issues

• Structure preserving numerical analysis of HIV/AIDS epidemic model  
  by Shah Zeb, Muhammad Bilal, Muhammad Rafiq, Siti Ainor Mohd Yatim, Zulfiqar Ali, Ayesha Kamran 
  Abstract: Human immunodeficiency virus (HIV) remains a major global health concern. This study presents a mathematical model using ordinary differential equations with a saturated incidence rate to analyse HIV transmission dynamics. The basic reproduction number R0 is derived, indicating disease-free equilibrium stability when R0<1, and endemic stability when R0 >1. Unlike conventional models, we employ structure-preserving numerical schemes to ensure biologically consistent solutions and unconditional stability. Two numerical approaches are developed: the standard finite difference (SFD) and non-standard finite difference (NSFD) methods. While SFD shows conditional convergence, the NSFD scheme provides unconditionally stable and positive solutions, even with large time steps. Numerical experiments confirm the accuracy and practicality of the proposed NSFD approach. This model and method can be extended to other infectious diseases, such as hepatitis and whooping cough, offering a robust tool for long-term epidemiological analysis and control strategy assessment.
  Keywords: human immunodeficiency virus; HIV; basic reproduction number; standard finite difference; SFD; non-standard finite difference; NSFD; stability analysis; comparison.
  DOI: 10.1504/IJMMNO.2025.10071899
   
  
• The new family of Ristić-Balakrishnan-type II Topp-Leone-heavy-tailed-G distribution with applications  
  by Oarabile Lekhane, Broderick Oluyede, Lesego Gabaitiri, Onkabetse Vincent Mabikwa 
  Abstract: We propose the new Ristić-Balakrishnan-type II Topp-Leone-heavy-tailed-G distribution. Some properties are derived including linear representation of the density function, probability weighted moments, R ényi entropy and distribution of order statistics. Several estimation methods are compared via simulation studies to establish the best method for parameter estimation of the new family of distributions. Actuarial measures are discussed and numerical studies are conducted to characterise the new family of distributions as heavy-tailed and its performance is validated using real data.
  Keywords: Ristić-Balakrishnan; type II Topp-Leone; heavy-tailed; simulation.
  DOI: 10.1504/IJMMNO.2025.10072140
   
  
• Transmission network expansion planning: best so far solution using hermit crab shell exchange algorithm  
  by Divya Rajoria, Ajay Sharma, Nirmala Sharma 
  Abstract: In this research, a recently developed meta-heuristic technique in the field of nature inspired algorithms (NIAs), namely, the hermit crab shell exchange (HCSE) algorithm is applied on the transmission network expansion planning (TNEP) problem. In this work, HCSE is applied with contingency-based security constrained TNEP (SeTNEP) with DCOPF for standard Graver's six bus test system and Brazilian 46 bus test system. Also TNEP with ACOPF for standard Graver's six bus test system and IEEE 24 bus test system is considered. The outcomes were evaluated against other renowned algorithms and deterministic methods that are available in the literature. The results reveal that the HCSE algorithm has accurately and proficiently solved the TNEP problem in these test scenarios.
  Keywords: DC optimal power flow; DCOPF; AC optimal power flow; ACOPF; meta-heuristic; hermit crab shell exchange algorithm; nature-inspired algorithms; NIAs; transmission network expansion planning; TNEP.
  DOI: 10.1504/IJMMNO.2025.10070730
   
  
• Analysing M/M/1 queue dynamics with system breakdowns and unreliable repair processes  
  by B. Janani, J. Kavitha 
  Abstract: A single server Markovian queueing paradigm is studied. The server is prone to random breakdowns when delivering service or during idle periods. When the server encountered problems, the repair procedure began immediately. The likelihood of restoring the server is p(p < 1) after an exponential repair time. All present users leave the system if the server cannot be fixed. The time-dependent likelihood for a single server queue with an unreliable repairer is explicitly estimated for the first time. The results were also cross-checked with the available literature. To demonstrate the significance of parameter values, performance measures and numerical figures were also supplied.
  Keywords: random breakdowns; unreliable repairer; time dependent probabilities; idle period; abandon.
  DOI: 10.1504/IJMMNO.2025.10071081
   
  
• Variance estimation for non-parametric regression model in systematic sampling under heteroscedastic errors: a simulation study  
  by Sana Wahid, Javaria Ahmad Khan, Atif Akbar 
  Abstract: Systematic sampling is an attractive tool for surveys as it is easily implemented and has an efficient design. In a systematic sample, an important problem is the unavailability of any direct estimator of design variance. A non-parametric model is flexible as it can be applied in different situations with auxiliary variables considered at the population level. Here, different estimators for a non-parametric model are considered for a given population using LPR as an estimation technique for multiple levels of heteroscedastic errors. For comparison, a simulation study is performed for different estimators. This comparison measures the relative bias and mean squared error. It is evident that the local polynomial non-parametric estimator performs well in our proposed situation.
  Keywords: non-parametric regression; variance estimation; heteroscedasticity; design-based method; systematic sampling; local polynomial regression.
  DOI: 10.1504/IJMMNO.2025.10071373
   
  
• Numerical analysis of heat loss from house roof and wall in winter to optimise energy consumption  
  by Ramola Sinha, Sangita Nitin Bansode 
  Abstract: The objective of this work is to estimate a transient heat loss from the roof/wall of a house during cold winter nights using transient FDM numerical method. Conventionally steady state conditions are assumed for estimating the building heating loads where the internal heat sources are neglected. However, the unsteady approach, by taking the internal heat sources into account, yields significantly small heating capacities and hence low initial costs. The solution used stability criteria using explicit method. Initially, the temperature of all nodes decreased at a faster rate and subsequently the convection, radiation, and total heat loss increased at a faster up to 400 min (or 6.67 hours) and then at a slower rate. The average heat loss estimated was 42.081 kW. The transient total heat loss varies between 16.53 kW to 60.0 kW in 12 hours. Numerical analysis provides accurate results, yields lower heating capacity and is economical for air conditioning design.
  Keywords: numerical method; finite difference method; transient heat transfer; explicit method; time step; stability criteria; convection heat loss; radiation heat loss; conduction heat loss; total heat loss.
  DOI: 10.1504/IJMMNO.2025.10071374
   
  
• Forward-backward transcritical bifurcation: control and optimisation in a novel fuzzy SIR model  
  by H.A. Bhavithra, S. Sindhuja, N. Ramalingam, S. Sindu Devi 
  Abstract: Understanding the dynamics of infectious disease spread is critical for effective public health interventions. Traditional epidemic models, such as SIR and SEIR, use deterministic parameters that often fail to account for real world uncertainty caused by incomplete data, behavioural variability, and evolving pathogens. Fuzzy logic provides a powerful alternative by treating parameters like transmission and recovery rates as fuzzy variables, enabling models to incorporate imprecision and better reflect reality. Originating in control theory, fuzzy logic has found applications in engineering, space science and uncertainty modelling. This study develops a fuzzy epidemic model using a utility-based framework, deriving a fuzzy disease-free equilibrium and a generalised basic reproduction number. Critical bifurcation points and sensitivity analyses highlights key transitions and intervention strategies. This approach enhances epidemic forecasting and decision making under uncertainty, offering a robust tool for managing complex health crises.
  Keywords: fuzzy deterministic model; forward bifurcation; backward bifurcation; transcritical bifurcation.
  DOI: 10.1504/IJMMNO.2025.10071124
   
  
• Modelling and analysis of VoIP call centre server performance with impatient callers, re-service, service interruption and buffer search  
  by R. Preena, D. Sumitha 
  Abstract: The paper investigates a retrial queueing scenario in a voice over internet protocol (VoIP) call centre. A single server with two stage service process is considered with the initial phase being the obligatory phase of service and the additional phase being the selective phase of service. The incoming calls arrive in multiple voice packets in accordance with the Poisson process. The system focuses on the behaviour of the caller and the server. Caller behaviour comprises of the impatient callers and callers opting for re-service. Server behaviour comprises of buffer search and service interruption followed by the immediate repair process. After the repair completion, the server continues the service for the interrupted caller. The steady state equations are framed for the system and performance measures are derived using supplementary variable technique. Numerical analysis and cost analysis are presented to analyse the performance of the system.
  Keywords: incoming calls; impatient caller; service interruption; re-service; buffer search.
  DOI: 10.1504/IJMMNO.2025.10071290