Modeling dynamics of cancer radiovirotherapy.

Advances in genetic engineering have paved the way for a new therapy for cancer, which is called virotherapy. This treatment uses genetically engineered viruses which selectively infect, replicate in, and destroy cancer cells without damaging normal cells. Furthermore, current research and clinical trials have indicated that these viruses can be delivered as single agents or in combination with other therapies. In this paper, we propose systems of ordinary differential equations for modeling the dynamics of aggressive tumor growth under radiovirotherapy treatment. We divide the treatment period into two phases; consequently, we present two mathematical models. First, we formulate the virotherapy model as Phase I of the treatment. Then we extend the model to include radiotherapy in combination with virotherapy as Phase II of the treatment. Comprehensive qualitative analyses of both models are conducted. Furthermore, numerical experiments are performed in order to support the analytical results. An analysis of the parameters is also carried out to investigate their effects on the outcome of the treatment. Overall, the analytical results reveal that radiovirotherapy is more effective than, and a good alternative to, virotherapy, as it is capable of eradicating tumors completely.

Modeling the effect of lockdown and social distancing on the spread of COVID-19 in Saudi Arabia.

The COVID-19 pandemic spread rapidly worldwide. On September 15, 2021, a total of 546,251 confirmed cases were recorded in Saudi Arabia alone. Saudi Arabia imposed various levels of lockdown and forced the community to implement social distancing. In this paper, we formulate a mathematical model to study the impact of these measures on COVID-19 spread. The model is analyzed qualitatively, producing two equilibrium points. The existence and stability of the COVID-19 free equilibrium and the endemic equilibrium depend on the control reproduction number, [Formula: see text]. These results are in good agreement with the numerical experiments. Moreover, the model is fitted with actual data from the COVID-19 dashboard of the Saudi Ministry of Health. We divide the timeline from March 12, 2020, to September 23, 2020, into seven phases according to the varied applications of lockdown and social distancing. We then explore several scenarios to investigate the optimal application of these measures and address whether it is possible to rely solely on social distancing without imposing a lockdown.

A time-delayed model for the spread of COVID-19 with vaccination.

A mathematical model is presented in this paper to investigate the effects of time delay in vaccine production on COVID-19 spread. The model is analyzed qualitatively and numerically. The qualitative analysis indicates that the system variables are non-negative, bounded, and biologically meaningful. Moreover, the model has produced two equilibrium points: the free equilibrium point, which can exist without conditions, and the endemic equilibrium point, which can exist if the control reproduction number, [Formula: see text], is not less than one. In addition, the local stability of the equilibrium points is investigated and agrees with the numerical analysis results. Finally, a sensitivity analysis is conducted for [Formula: see text]. In particular, we examine the effect of the vaccine's time delay, vaccine rate, and vaccine efficiency on the model dynamics.

Modeling the effect of random diagnoses on the spread of COVID-19 in Saudi Arabia.

Saudi Arabia was among the countries that attempted to manage the COVID-19 pandemic by developing strategies to control the epidemic. Lockdown, social distancing and random diagnostic tests are among these strategies. In this study, we formulated a mathematical model to investigate the impact of employing random diagnostic tests to detect asymptomatic COVID-19 patients. The model has been examined qualitatively and numerically. Two equilibrium points were obtained: the COVID-19 free equilibrium and the COVID-19 endemic equilibrium. The local and global asymptotic stability of the equilibrium points depends on the control reproduction number Rc. The model was validated by employing the Saudi Ministry of Health COVID-19 dashboard data. Numerical simulations were conducted to substantiate the qualitative results. Further, sensitivity analysis was performed on Rc to scrutinize the significant parameters for combating COVID-19. Finally, different scenarios for implementing random diagnostic tests were explored numerically along with the control strategies applied in Saudi Arabia.