Objective Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number . The model equations are solved numerically using fourth and fifth order Runge–Kutta methods. Results We found an of 2.03, implying that the pandemic will persist in the human population in the absence of strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread on novel coronavirus.

Objective: Coronavirus disease 2019 (COVID-19) is a pandemic of respiratory disease spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study is to apply SEIR compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number R0. The model equations are solved numerically using fourth and fifth order Runge–Kutta methods. Results: The value of basic reproduction number R0 was determined as 2.03, implying that the pandemic will persist in the human population. Results after simulating various scenarios indicate that disregarding social distancing, wearing of masks and frequent washing of hands can have devastating effects on the human population. The model shows that quarantine and isolation are key winners to this pandemic.

Objective: Coronavirus disease 2019 (COVID-19) is a pandemic respiratory illness spreading from person-to-person caused by a novel coronavirus and poses a serious public health risk. The goal of this study was to apply a modified susceptible-exposed-infectious-recovered (SEIR) compartmental mathematical model for prediction of COVID-19 epidemic dynamics incorporating pathogen in the environment and interventions. The next generation matrix approach was used to determine the basic reproduction number (O). The model equations are solved numerically using fourth and fifth order Runge Kutta methods.Results: We found an b of j, implying that the pandemic will persist in the human population absent strong control measures. Results after simulating various scenarios indicate that disregarding social distancing and hygiene measures can have devastating effects on the human population. The model shows that quarantine of contacts and isolation of cases can help halt the spread of novel coronavirus.

In this paper, we develop a mathematical model describing the dynamics of HIV transmission by incorporating sexual orientation of individuals. Equilibrium points and the basic reproduction number are derived. The basic reproduction number provides a threshold that determines whether or not the disease fades away. The model, described by non-linear ODEs, shows existence of unique diseasefree and disease-persistent equilibria. Least squares curve fitting is presented to quantitatively investigate the trend of infection within each gender. The results are indicative of a higher infectivity in the female population. We further investigated the effect of the introduction of pre-exposure prophylaxis (PrEP) on the dynamics of the HIV. Our results show that the introduction of PrEP has had a positive effect on the limitation of spread of HIV. Sensitivity analysis results show that control of effective contacts can result in control of the disease across gender divide. The model provides a unique opportunity to influence policy on HIV treatment and management.

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Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

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