Neural network modeling of Lassa fever spread and disability effects.

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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Apr 11;16:17093. doi: 10.1038/s41598-026-47581-9 Neural network modeling of Lassa fever spread and disability effects Zulqurnain Sabir 1, ✉ , M A Abdelkawy 2 , Maros Jakubec 3 , Nora yehia Ibrahim 4 , Ashour M Ahmed 5 , Mustafa Bayram 2, 6 , Harun Çiçek 3, 7 Author information Article notes Copyright and License information 1 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon 2 Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11989 Saudi Arabia 3 University Science Park UNIZA, University of Žilina, Univerzitná 8215/1, Žilina, 010 26 Slovakia 4 Electronic Research Institute (ERI), Cairo, Egypt 5 Physics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11623 Saudi Arabia 6 Department of Computer Engineering, Biruni University, Istanbul, 34010 Turkey 7 Faculty of Science and Arts, Department of Mathematics, Bitlis Eren University, Bitlis, 13000 Turkey ✉ Corresponding author. Received 2025 Oct 15; Accepted 2026 Apr 1; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13230529  PMID: 41965428 Abstract Lassa fever is one of the viral hemorrhagic illnesses produced through the Lassa virus and may be transmitted to individuals via contact with diseased rodents or their feces and urine. The current study presents the solutions to the nonlinear zoonotic spread of Lassa virus fever leading to disabilities model by designing a supervised neural network. The model is divided into the human (susceptible, severely infected, mildly infected, and recovered) and rodent (susceptible, infected) populations. The dynamic structure of one class to the other performs the zoonotic spread of Lassa virus fever model makes nonlinear. A dataset via Runge-Kutta is obtained, which decreases the mean square error by dividing the training, validation, and testing with 78%, 12% and 10%. The proposed neural network construction is designed with a single hidden layer keeping 20 neurons and sigmoid function, while Bayesian regularization is used for the optimization. The designed neural network scheme’s reliability is obtained using different tests including best training values, correlation performances, state transition, and error histogram. The correctness of the designed neural network solver is observed through the matching of the proposed and Runge-Kutta outputs, and insignificant absolute error calculated as 10 − 02 to 10 − 03 . Keywords: Lassa virus fever model, Disabilities, Neural network, Bayesian regularization, Optimization Subject terms: Computational biology and bioinformatics, Diseases, Mathematics and computing Introduction Human diseases are frequently recognized by different symptoms such as suffering, pain, dysfunction, or mortality. Because they have a chance to produce considerable contagion and death, infectious diseases can be disseminated in either the direct or indirect way by microorganisms that pose serious threats to the world’s health 1 . A zoonotic illness that is produced or reappeared in several West African nations, such as Sierra Leone, Ghana, Togo, Liberia, Nigeria, Guinea, and Benin is Lassa fever (LF) 2 . LF is one of the zoonotic diseases, which means it transmits between humans and animals 3 . LF initially spreads through the contact of diseased rodents, their urine or feces. In the West Africa region, the illness is endemic, and individuals frequently experience contact with infected rodents while conducting foodstuffs that have been polluted with rodent feces or urine 4 . This zoonotic conduction can lead to severe implications, like respiratory distress, hemorrhagic fever, and even death. The overwhelming consequences of LF are to produce longstanding disabilities. Nigeria recorded 211 laboratory confirmed cases of LF from January 3 to 30, 2022, which resulted in forty-total mortality 5 . The incidents spread throughout the federal capital region and 14 out of 36 states in Nigeria, which makes up a sizable chunk of the nation. The LF survivors can face enduring harm to their hearing, cognitive function or vision. Some of the reports also indicate that LF produces brain inflammation, leading to tremors, seizures, and other nervous indications 6 . These disabilities present significant effects on the quality of life, which make it challenging for them to attend school, work, or contribute to regular activities. The zoonotic banquet of LF highlights the essentials through education and awareness about the illness, mainly in rural groups where the danger of spreading is high. By endorsing proper hygiene practices, such as storage of food in rodent-proof vessels and evading interaction with hypothetically diseased rodents, persons can decrease their danger of constricting the illness. Moreover, healthcare suppliers must be qualified to identify the symptoms of LF and deliver rapid action to avoid lasting disabilities and lessen the mortality risk 7 . Prior to spreading to other tissues, this viral infection first attacks immune systems in the nasal cavity then moving on to neighboring lymph glands. The illness progresses in a variety of ways after an incubation time frame of one to three weeks. More serious instances may come with a variety of indicators, such as pulmonary edema, low blood pressure, and diarrhea; however, the majority of individuals only have minor signs including low-grade fever, malaise, and headache 8 . According to Khan et al. 9 , a little portion might show blood leaking through the genitalia, rectum, or oropharynx. Most prevalent neurological impairment seen in LF individuals is hearing loss. However certain studies contend that this estimate may be overestimated; statistics indicate that this consequence impacts between one quarter and one-third of patients who sustain the disease 10 . It is important to note that deafness usually happens in the postoperative stage of the sickness, regardless of whether the individual has fully recovered, suggesting that this disease may be caused by an immune process as opposed to having a viral origin 11 . This hearing loss occurs in just over 50% of instances and may impact one ear. The disabilities based on the infrequent central nervous system are produced by LF, which contain encephalitis, sensorineural deafness, recuperative ataxia, prolonged neuropsychiatric appearances (like psychosis, depression, mania, asthenia, cognitive impairments, and sleep disturbances), meningitis, coma, and seizures. These neurological signs tend to be less frequent than LF’s more prevalent generalized symptoms 12 , 13 . Moreover, the mathematical model has been studied in various applications, some of them are Yunus et al. 14 provided a fractional mathematical system for understanding and controlling communication dynamics in the management systems of computer viruses. Oqielat et al. 15 examined a structure of fractional series explanations for fractional diffusion reaction for the growth system of bacteria through Laplace residual power series scheme. Khan et al. 16 provided the nonlinear dynamics based on the piecewise modified ABC fractional leukemia system with symmetric numerical imitations. The current research investigations provide the numerical solutions to the nonlinear zoonotic spread of LF leading to disabilities by designing a single structure of the hidden layer is used by relating the sigmoid function. The optimization is assessed by the Bayesian regularization neural network (ByRNN), which has never been exploited before for solving the nonlinear zoonotic spread of the LF leading to disabilities model. However the existing investigations that use the conventional compartmental schemes, the designed ByRNN structure capture intricate relations between rodent and human populations. In current decades, the neural network schemes have been applied in a variety of nonlinear biological and stiff applications, like singular 5th nonlinear multi-pantograph differential system 17 , fractional environmental/economic system 18 , acute respiratory syndrome coronavirus model 19 , hard water consumption of kidney function 20 , and singular two-point nonlinear system based on thermal-explosion theory 21 . Moreover, the neural network studies is applied in other application, e.g., Anwer et al. 22 provided the machine intelligent expedition together with supervised Bayesian adaptive neural networks for solving the stochastic cholera epidemic system in a periodic environment. In another study, Anwar et al. 23 studies a stochastic adaptive autoregressive eXogenous networks operative with Grünwald Letnikove fractional finite differences based on the nonlinear fractal differential framework of coffee rust control system. They also applied the neural network structures in the solutions of computer virus model 24 , and nonlinear measles transmission system with impact of immunization 25 . Some novelty points of this study are shown as: It is always stimulating to deal with the nonlinear models using traditional schemes. Therefore, one of the operational methods for presenting the solutions of complex models is the proposed ByRNN. To investigate the designed supervised stochastic ByRNN scheme, the numerical representations have been effectively provided for the zoonotic spread of LF leading to disabilities. The exactness of the scheme correctness is performed via outputs matching as well as insignificant absolute error (AE). Different tests based on the state transition (ST), correlation, and error histogram (EH) are provided to authenticate the solver’s accuracy. The organization of the paper is provided as: Mathematical nonlinear zoonotic spread of LF leading to disabilities system is given in Sect. 2 , a process of ByRNN is presented in Sect. 3 , the outcomes of the model are discussed in Sect. 4 , and the final comments are presented in Sect. 5 . Zoonotic spread of LF model The mathematical nonlinear zoonotic spread of the LF model leading to disabilities is separated into the population of humans and rodents. The population of individuals is categorized into susceptible , mildly infected , severely infected , and recovered individuals , while the rodent population is classified into susceptible and infected rodents . The mathematical form of the model is given as 8 : 1 The model is divided into human and rodent compartments, the details of human classes are given as: Susceptible (S(u)) : People at danger of contracting LF through contact with diseased rodents. Mildly infected (I m (u)) : People having mild signs expected to improve without treatment. Severely infected (I s (u)) : Those having severe indications, potentially demanding and at a higher threat of disability or death. Recovered (R(u)) : Those who got recovery, possibly without or with enduring disabilities. The details of rodent groups are presented as: Susceptible (S r (u)) : Those at danger of getting LF via interaction with diseased rodents. Infected (Ir(u)) : Rodents transmitting and carrying LF to people. The parameters used in the above system are defined as: Π shows the human population rate. The comparative transmissibility from one to another human in insignificant and rigorous infected classes is signified by β m and β s . The rate of transition through the mild to severe class is represented by γ . The rate of comparative spreading through rodents to people is represented as α m and α s , whereas the rate of comparative recovery is given as ρ m and ρ s . Based on the rodent’s population, Λ presents the rate of recruitment, and ϕ is the spreading rate in the rodents, while ξ and ν and are the rates of mortality in the populations of rodent and human. Moreover, , , , , , and are the initial conditions (ICs). The schematic illustration of the LF model shown in Fig. 1 . Fig. 1. Open in a new tab Schematic illustrations of the LF model leading to disabilities. Some epidemiological assumptions, which are used in the above mathematical system are given as: The population of humans is separated into four classes: susceptible, severely infected, mildly infected, and recovered, with clear transitions. The population of rodents is categorized into two groups: infected and susceptible, with spread occurring between humans and rodents. Spread happens via interaction with infected rodents, with a stated rate of spread. Infected individuals can improve without or with disabilities, manipulating spread dynamics and results. The system undertakes a constant contact rate between rodents and humans, spatial, neglecting age, or interactive heterogeneities. Methodology In this section, the supervised neural network based on ByRNN by using twenty neurons and the sigmoid function in the hidden layer is presented as: 2 3 where w and ῳ are the weights, b and B present the biases, while S ( u ), I m ( u ), I s ( u ), R ( u ), S r ( u ) and I r ( u ) are the output values. Moreover, is the log-sigmoid activation function, which is given as: 4 The log-sigmoid function or logistic is a mathematical function, which draws any real value between 0 and 1. This function is normally implemented in machine learning and artificial neural networks as a merit function. The key advantage of this function is to deal with the nonlinearity, which provides the support to understand complicated relations in inputs and outputs. The differentiable values of the logistic function are easy to optimize. This function is also implemented to work with other functions, like tanh or radial basis functions to perform more rapid model’s outputs. The progressive execution of the ByRNN is performed in order to train and develop the primary hidden layer. The ByRNN technique distributes complexity to assess the stochastic Bayesian in order to attain the learning values through the outputs of its features. The workflow diagram is shown in Fig. 2 that is related to the model, neural structure and some results. The command “nftool” in the MATLAB software is used to present the optimization through ByRNN. The remaining setting in the feed-forward process of the neural network contains step size 1/100; tolerance 10 − 07 ; 1000 epochs; n -folded cross-validation; 20 neurons; and sigmoid activation function. The dataset is separated into the sets of training as 78%, testing as 10%, and validation as 12%. The execution of the set of training is used for the progress of the model, set of testing is used for hyperparameter tuning, and set of validation is applied to evaluate the performance of the neural network. For the simulations of the results, MATLAB R2019a is used. Fig. 2. Open in a new tab Workflow diagram for the LF model leading to disabilities. Figure 3 presents the layer structure of the nonlinear zoonotic spread of Lassa virus fever model leading to disabilities by using the ByRNN. Six outputs are achieved using the ByRNN, the curve presented in the box of hidden layer shows the sigmoid function and 20 neurons, while w and b are the weights and bias. Fig. 3. Open in a new tab A single hidden layer structure for solving the LF model leading to disabilities. Some potential limitations of this study are given as: The system undertakes a basic separation of populations based on the human and rodent, possibly managing significant heterogeneities or sub-groups. The system emphasises on the spreading of rodent-to-human, abandoning potential one to other human communication or other directions. The correctness of the system depends on parameter approximations, which might not imitate real-world performances. The hidden-single-layer construction might be inadequate to perform intricate nonlinear associations. The values of AE around 10 − 02 to 10 − 03 might be momentary in certain settings, controlling the predictive power of the system. Discussion of results The numerical results of the zoonotic spread of Lassa virus fever model by implementing ByRNN process are provided in two cases as: Case 1 : Consider the values , , , , , , , , , , and , while the ICs are 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 used in system (1) as 8 : 5 Case 2 : Consider the values , , , , , , , , , , and , while the ICs are 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 used in system (1) as 8 : 6 Figures 4 , 5 , 6 and 7 present the numerical performances of the nonlinear zoonotic spread of Lassa virus fever model by implementing the ByRNN process. Figure 4 a,b presents optimal verification and transition state (TS) for solving the nonlinear zoonotic spread of the Lassa virus fever model. The optimal performances of training are presented to decrease the mean square error (MSE) at iterations 1000 for both cases. The optimal training performances are signified as 2.023 × 10 − 05 , and 5.6626 × 10 − 05 for the nonlinear zoonotic spread of Lassa virus fever model. The best neuron values are performed through cross-validation and testing, which supports the context in efficiently detecting deviation, balancing bias, nonlinear actions, and concealed data generalizing. The design of a neural network presents the lowest MSE findings generally pointing to a critical area for assessing the system’s dependability. The gradient measures are performed in Fig. 4 c,d for solving the model. These values have been performed to check the arrangement’s convergence outcomes. The process of supervised neural network scheme is implemented to lessen the MSE training by providing largely functional gradient competencies. The outcomes based on the fitting curve for solving the Lassa virus fever model by implementing the ByRNN process are reported in Fig. 5 a,b. The proposed stochastic ByRNN process is applied to correlate the outputs of the nonlinear Lassa virus fever model, considering the most successful results. Figure 5 c,d presents the performances of error histogram (EH) that are calculated as 2.014 × 10 − 03 and 3.299 × 10 − 03 for the nonlinear Lassa virus fever model. Since EH depends on bias identification, network evaluations, and error levels, it is considered useful to get quick inputs in this supervised neural network. EH, which assesses neural network capacity, is a useful method for evaluating and enhancing foundations. The nonlinear zoonotic spread of Lassa virus fever system’s correlation illustrations are presented in Figs. 6 and 7 . These regression representations determine the robust process and the components of the desired outcome by linking the results to scores. Correlation coefficient ( R 2 ) relating the regression and the response variable is calculated as 1 for both cases of the nonlinear Lassa virus fever model that represents the scheme’s accuracy. Table 1 presents the different performances of the nonlinear Lassa virus fever model. Fig. 4. Open in a new tab The values based best training ( a , b ) and gradient ( c , d ) for the nonlinear Lassa virus fever model. Fig. 5. Open in a new tab Fitness ( a , b ) and EH ( c , d ) values for the nonlinear Lassa virus fever model. Fig. 6. Open in a new tab Regression for nonlinear Lassa virus fever model based case (1). Fig. 7. Open in a new tab Regression for nonlinear Lassa virus fever model based case (2). Table 1. Different test presentations for the nonlinear Lassa virus fever. Case M.S.E Testing Training Performance Epochs Time 1 5.50186 × 10 − 05 2.02297 × 10 − 05 2.02 × 10 − 05 1000 iterations 10 s 2 1.74105 × 10 − 04 5.66262 × 10 − 05 5.66 × 10 − 05 1000 iterations 10 s Open in a new tab The nonlinear Lassa virus fever model is solved numerically using the design of a supervised neural network together with the ByRNN, as illustrated in Fig. 8 . The matching of outputs is depicted for both cases of the nonlinear Lassa virus fever model. The accuracy of the ByRNN for solving the nonlinear Lassa virus fever model is designated by these proposed and referenced outputs. Figure 9 presents the AE for solving both cases of the nonlinear Lassa virus fever model, which performs that these measures are calculated as 10 − 03 to 10 − 04 . These insignificant AE performances for both models’ cases progress the dependability of the designed supervised ByRNN. Fig. 8. Open in a new tab Outputs for both cases of the nonlinear Lassa virus fever model. Fig. 9. Open in a new tab AE for both cases of the nonlinear Lassa virus fever model. Conclusion In the current study, the numerical solutions of the nonlinear zoonotic spread of Lassa virus fever leading to disabilities have been performed by designing a stochastic computing infrastructure of a supervised neural network. The nonlinear zoonotic spread of Lassa virus fever system leading to disabilities is divided into the human (susceptible, mildly infected, severely infected, and recovered individuals) and rodent (susceptible, and infected) populations. Some concluding remarks of this work are presented as: The efficient demonstration of supervised neural networks is performed for the nonlinear zoonotic spread of the LF model. The outcomes of the system matched reference results with AE 10 − 02 to 10 − 03 , which show the accuracy of the scheme. The consistency of the proposed neural network has been recognized from different assessments, like EH and correlation measures. The optimization is performed through the Bayesian regularization, which is significant for nonlinear systems as it avoids overfitting and advances generalization based on the previous information. The performance of the model is improved by selecting the data from 78% training, 10% testing, and 12% validation. A process of one-hidden layer with sigmoid activation function and 20 neurons effectively exhibited the dynamics of LF. Some tests including regression values and EH have also been used to authenticate the reliability of the proposed solver. In future the designed ByRNN process can be used to solve other diverse applications, some of them are fluid dynamical systems, singular coupled Lane-Emden models, human head problems, predator-prey models, cancer disease systems, corneal shape models, and fractional order virus models. Author contributions Zulqurnain Sabir, M A Abdelkawy, Maros Jakubec, Nora yehia Ibrahim, Ashour M. Ahmed, Mustafa Bayram, Harun ÇİÇEK contributed equally to prepare this manuscript. Funding This work was supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud IslamicUniversity (IMSIU) (grant number IMSIU-DDRSP2602). Data availability The dataset used and/or analysed during the current study available from the corresponding author on reasonable request. Declarations Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References 1. Ojo, M. M., Gbadamosi, B., Benson, T. O., Adebimpe, O. & Georgina, A. L. Modeling the dynamics of Lassa fever in Nigeria. J. Egypt. Math. Soc. 29 , 1–19 (2021). [ Google Scholar ] 2. Elughi, G. N. et al. Computational Approaches Toward Prevention and Surveillance of Lassa Fever in Developing Countries. In Biotechnological Approaches to Sustainable Development Goals 145–157 (Springer Nature Switzerland, 2023). [ Google Scholar ] 3. Madueme, P. G. U. & Chirove, F. Understanding the transmission pathways of Lassa fever: A mathematical modeling approach. Infect. Dis. Model. 8 (1), 27–57 (2023). 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