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Papers by Mahmoud Ibrahim

Research paper thumbnail of A seasonal model to assess intervention strategies for preventing periodic recurrence of Lassa fever

Heliyon, 2021

Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens pri... more Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens prioritized for research and development, affecting several hundreds of thousands of people each year. Lassa fever is spread via infected Natal multimammate mice and also through human-to-human contacts and it is a particular threat to pregnant women. Despite its importance, relatively few mathematical models have been established for modelling Lassa fever transmission up to now. We establish and study a new compartmental model for Lassa fever transmission including asymptomatic carriers, quarantine and periodic coefficients to model annual weather changes. We determine parameter values providing the best fit to data from Nigerian states Edo and Ondo from 2018-20. We perform uncertainty analysis and PRCC analysis to assess the importance of different parameters and numerical simulations to estimate the possible effects of control measures in eradicating the disease. The results suggest that the most important parameter which might be subject of control measures is death rate of mice, while mouse-to-human and human-to-human transmission rates also significantly influence the number of infected. However, decreasing the latter two parameters seems insufficient to eradicate the disease, while a parallel application of decreasing transmission rates and increasing mouse death rate might be able to stop the epidemic.

Research paper thumbnail of Threshold and stability results in a periodic model for malaria transmission with partial immunity in humans

Applied Mathematics and Computation, 2021

We develop a periodic compartmental population model for the spread of malaria, dividing the huma... more We develop a periodic compartmental population model for the spread of malaria, dividing the human population into two classes: non-immune and semi-immune. The effect of seasonal changes in weather on the malaria transmission is considered by applying a non-autonomous model where mosquito birth, death and biting rates are time-dependent. We show that the global dynamics of the system is determined by the basic reproduction number, which we define as the spectral radius of a linear integral operator. For values of the basic reproduction number less than unity, the disease-free periodic solution is globally asymptotically stable, while if R 0 > 1 , then the disease remains endemic in the population. We show simulations in accordance with the analytic results. Finally, we show that the time-average reproduction rate gives an underestimation for malaria transmission risk.

Research paper thumbnail of A mathematical model for Lassa fever transmission dynamics in a seasonal environment with a view to the 2017–20 epidemic in Nigeria

Nonlinear Analysis: Real World Applications, 2021

Research paper thumbnail of Predicting the COVID-19 Spread Using Compartmental Model and Extreme Value Theory with Application to Egypt and Iraq

Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, 2021

In this chapter, we study and investigate the spread of coronavirus disease 2019 (COVID-19) in Ir... more In this chapter, we study and investigate the spread of coronavirus disease 2019 (COVID-19) in Iraq and Egypt by using compartmental, logistic regression, and Gaussian models. We developed a generalized SEIR model for the spread of COVID-19 considering mildly and symptomatically infected. The logistic and Gaussian models were utilized to forecast and predict the number of confirmed cases from both countries. We estimate the parameters that give the best fit to the incidence data, and the results provide severe forecasts for Iraq and Egypt. To provide a forecast of the spread of COVID-19 in Iraq, we present various simulation scenarios for the expected peak and its time by using Gaussian and logistic regression models, and a reasonable concord with officially reported cases was shown by the forecasted cases. Our sensitivity analyses of the basic reproduction number conclude that the most effective way to prevent COVID-19 cases is decreasing the transmission rate. The findings of this...

Research paper thumbnail of Impact of weather seasonality and sexual transmission on the spread of Zika fever

Scientific Reports

We establish a compartmental model to study the transmission of Zika virus disease including spre... more We establish a compartmental model to study the transmission of Zika virus disease including spread through sexual contacts and the role of asymptomatic carriers. To incorporate the impact of the seasonality of weather on the spread of Zika, we apply a nonautonomous model with time-dependent mosquito birth rate and biting rate, which allows us to explain the differing outcome of the epidemic in different countries of South America: using Latin Hypercube Sampling for fitting, we were able to reproduce the different outcomes of the disease in various countries. Sensitivity analysis shows that, although the most important factors in Zika transmission are the birth rate of mosquitoes and the transmission rate from mosquitoes to humans, spread through sexual contacts also highly contributes to the transmission of Zika virus: our study suggests that the practice of safe sex among those who have possibly contracted the disease, can significantly reduce the number of Zika cases.

Research paper thumbnail of Modeling, Control, and Prediction of the Spread of COVID-19 Using Compartmental, Logistic, and Gauss Models: A Case Study in Iraq and Egypt

Processes

In this paper, we study and investigate the spread of the coronavirus disease 2019 (COVID-19) in ... more In this paper, we study and investigate the spread of the coronavirus disease 2019 (COVID-19) in Iraq and Egypt by using compartmental, logistic regression, and Gaussian models. We developed a generalized SEIR model for the spread of COVID-19, taking into account mildly and symptomatically infected individuals. The logistic and Gaussian models were utilized to forecast and predict the numbers of confirmed cases in both countries. We estimated the parameters that best fit the incidence data. The results provide discouraging forecasts for Iraq from 22 February to 8 October 2020 and for Egypt from 15 February to 8 October 2020. To provide a forecast of the spread of COVID-19 in Iraq, we present various simulation scenarios for the expected peak and its timing using Gaussian and logistic regression models, where the predicted cases showed a reasonable agreement with the officially reported cases. We apply our compartmental model with a time-periodic transmission rate to predict the poss...

Research paper thumbnail of Global dynamics of a mathematical model for a honeybee colony infested by virus-carrying Varroa mites

Journal of Applied Mathematics and Computing

We establish a new four-dimensional system of differential equations for a honeybee colony to sim... more We establish a new four-dimensional system of differential equations for a honeybee colony to simultaneously model the spread of Varroa mites among the bees and the spread of a virus transmitted by the mites. The bee population is divided to forager and hive bees, while the latter are further divided into three compartments: susceptibles, those infested by non-infectious vectors and those infested by infectious vectors. The system has four potential equilibria. We identify three reproduction numbers that determine the global asymptotic stability of the four possible equilibria. By using Dulac's criterion, Poincaré-Bendixson and persistence theory, we show that the solutions always converge to one of the equilibria, depending on those three reproduction numbers. Hence we completely describe the global dynamics of the system.

Research paper thumbnail of A seasonal model to assess intervention strategies for preventing periodic recurrence of Lassa fever

Heliyon, 2021

Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens pri... more Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens prioritized for research and development, affecting several hundreds of thousands of people each year. Lassa fever is spread via infected Natal multimammate mice and also through human-to-human contacts and it is a particular threat to pregnant women. Despite its importance, relatively few mathematical models have been established for modelling Lassa fever transmission up to now. We establish and study a new compartmental model for Lassa fever transmission including asymptomatic carriers, quarantine and periodic coefficients to model annual weather changes. We determine parameter values providing the best fit to data from Nigerian states Edo and Ondo from 2018-20. We perform uncertainty analysis and PRCC analysis to assess the importance of different parameters and numerical simulations to estimate the possible effects of control measures in eradicating the disease. The results suggest that the most important parameter which might be subject of control measures is death rate of mice, while mouse-to-human and human-to-human transmission rates also significantly influence the number of infected. However, decreasing the latter two parameters seems insufficient to eradicate the disease, while a parallel application of decreasing transmission rates and increasing mouse death rate might be able to stop the epidemic.

Research paper thumbnail of A seasonal model to assess intervention strategies for preventing periodic recurrence of Lassa fever

Heliyon, 2021

Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens pri... more Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens prioritized for research and development, affecting several hundreds of thousands of people each year. Lassa fever is spread via infected Natal multimammate mice and also through human-to-human contacts and it is a particular threat to pregnant women. Despite its importance, relatively few mathematical models have been established for modelling Lassa fever transmission up to now. We establish and study a new compartmental model for Lassa fever transmission including asymptomatic carriers, quarantine and periodic coefficients to model annual weather changes. We determine parameter values providing the best fit to data from Nigerian states Edo and Ondo from 2018-20. We perform uncertainty analysis and PRCC analysis to assess the importance of different parameters and numerical simulations to estimate the possible effects of control measures in eradicating the disease. The results suggest that the most important parameter which might be subject of control measures is death rate of mice, while mouse-to-human and human-to-human transmission rates also significantly influence the number of infected. However, decreasing the latter two parameters seems insufficient to eradicate the disease, while a parallel application of decreasing transmission rates and increasing mouse death rate might be able to stop the epidemic.

Research paper thumbnail of Threshold and stability results in a periodic model for malaria transmission with partial immunity in humans

Applied Mathematics and Computation, 2021

We develop a periodic compartmental population model for the spread of malaria, dividing the huma... more We develop a periodic compartmental population model for the spread of malaria, dividing the human population into two classes: non-immune and semi-immune. The effect of seasonal changes in weather on the malaria transmission is considered by applying a non-autonomous model where mosquito birth, death and biting rates are time-dependent. We show that the global dynamics of the system is determined by the basic reproduction number, which we define as the spectral radius of a linear integral operator. For values of the basic reproduction number less than unity, the disease-free periodic solution is globally asymptotically stable, while if R 0 > 1 , then the disease remains endemic in the population. We show simulations in accordance with the analytic results. Finally, we show that the time-average reproduction rate gives an underestimation for malaria transmission risk.

Research paper thumbnail of A mathematical model for Lassa fever transmission dynamics in a seasonal environment with a view to the 2017–20 epidemic in Nigeria

Nonlinear Analysis: Real World Applications, 2021

Research paper thumbnail of Predicting the COVID-19 Spread Using Compartmental Model and Extreme Value Theory with Application to Egypt and Iraq

Trends in Biomathematics: Chaos and Control in Epidemics, Ecosystems, and Cells, 2021

In this chapter, we study and investigate the spread of coronavirus disease 2019 (COVID-19) in Ir... more In this chapter, we study and investigate the spread of coronavirus disease 2019 (COVID-19) in Iraq and Egypt by using compartmental, logistic regression, and Gaussian models. We developed a generalized SEIR model for the spread of COVID-19 considering mildly and symptomatically infected. The logistic and Gaussian models were utilized to forecast and predict the number of confirmed cases from both countries. We estimate the parameters that give the best fit to the incidence data, and the results provide severe forecasts for Iraq and Egypt. To provide a forecast of the spread of COVID-19 in Iraq, we present various simulation scenarios for the expected peak and its time by using Gaussian and logistic regression models, and a reasonable concord with officially reported cases was shown by the forecasted cases. Our sensitivity analyses of the basic reproduction number conclude that the most effective way to prevent COVID-19 cases is decreasing the transmission rate. The findings of this...

Research paper thumbnail of Impact of weather seasonality and sexual transmission on the spread of Zika fever

Scientific Reports

We establish a compartmental model to study the transmission of Zika virus disease including spre... more We establish a compartmental model to study the transmission of Zika virus disease including spread through sexual contacts and the role of asymptomatic carriers. To incorporate the impact of the seasonality of weather on the spread of Zika, we apply a nonautonomous model with time-dependent mosquito birth rate and biting rate, which allows us to explain the differing outcome of the epidemic in different countries of South America: using Latin Hypercube Sampling for fitting, we were able to reproduce the different outcomes of the disease in various countries. Sensitivity analysis shows that, although the most important factors in Zika transmission are the birth rate of mosquitoes and the transmission rate from mosquitoes to humans, spread through sexual contacts also highly contributes to the transmission of Zika virus: our study suggests that the practice of safe sex among those who have possibly contracted the disease, can significantly reduce the number of Zika cases.

Research paper thumbnail of Modeling, Control, and Prediction of the Spread of COVID-19 Using Compartmental, Logistic, and Gauss Models: A Case Study in Iraq and Egypt

Processes

In this paper, we study and investigate the spread of the coronavirus disease 2019 (COVID-19) in ... more In this paper, we study and investigate the spread of the coronavirus disease 2019 (COVID-19) in Iraq and Egypt by using compartmental, logistic regression, and Gaussian models. We developed a generalized SEIR model for the spread of COVID-19, taking into account mildly and symptomatically infected individuals. The logistic and Gaussian models were utilized to forecast and predict the numbers of confirmed cases in both countries. We estimated the parameters that best fit the incidence data. The results provide discouraging forecasts for Iraq from 22 February to 8 October 2020 and for Egypt from 15 February to 8 October 2020. To provide a forecast of the spread of COVID-19 in Iraq, we present various simulation scenarios for the expected peak and its timing using Gaussian and logistic regression models, where the predicted cases showed a reasonable agreement with the officially reported cases. We apply our compartmental model with a time-periodic transmission rate to predict the poss...

Research paper thumbnail of Global dynamics of a mathematical model for a honeybee colony infested by virus-carrying Varroa mites

Journal of Applied Mathematics and Computing

We establish a new four-dimensional system of differential equations for a honeybee colony to sim... more We establish a new four-dimensional system of differential equations for a honeybee colony to simultaneously model the spread of Varroa mites among the bees and the spread of a virus transmitted by the mites. The bee population is divided to forager and hive bees, while the latter are further divided into three compartments: susceptibles, those infested by non-infectious vectors and those infested by infectious vectors. The system has four potential equilibria. We identify three reproduction numbers that determine the global asymptotic stability of the four possible equilibria. By using Dulac's criterion, Poincaré-Bendixson and persistence theory, we show that the solutions always converge to one of the equilibria, depending on those three reproduction numbers. Hence we completely describe the global dynamics of the system.

Research paper thumbnail of A seasonal model to assess intervention strategies for preventing periodic recurrence of Lassa fever

Heliyon, 2021

Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens pri... more Lassa haemorrhagic fever is listed in WHO's Blueprint priority list of diseases and pathogens prioritized for research and development, affecting several hundreds of thousands of people each year. Lassa fever is spread via infected Natal multimammate mice and also through human-to-human contacts and it is a particular threat to pregnant women. Despite its importance, relatively few mathematical models have been established for modelling Lassa fever transmission up to now. We establish and study a new compartmental model for Lassa fever transmission including asymptomatic carriers, quarantine and periodic coefficients to model annual weather changes. We determine parameter values providing the best fit to data from Nigerian states Edo and Ondo from 2018-20. We perform uncertainty analysis and PRCC analysis to assess the importance of different parameters and numerical simulations to estimate the possible effects of control measures in eradicating the disease. The results suggest that the most important parameter which might be subject of control measures is death rate of mice, while mouse-to-human and human-to-human transmission rates also significantly influence the number of infected. However, decreasing the latter two parameters seems insufficient to eradicate the disease, while a parallel application of decreasing transmission rates and increasing mouse death rate might be able to stop the epidemic.