Monkeypox (MPX), similar to both smallpox and cowpox, is caused by the monkeypox virus (MPXV). It occurs mostly in remote Central and West African communities, close to tropical rain forests. It is caused by the monkeypox virus in the Poxviridae family, which belongs to the genus Orthopoxvirus. We develop and analyse a deterministic mathematical model for the monkeypox virus. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. It is shown that the model undergo backward bifurcation, where the locally stable disease-free equilibrium coexists with an endemic equilibrium. Furthermore, we determine conditions under which the disease-free equilibrium of the model is globally asymptotically stable. Finally, numerical simulations to demonstrate our findings and brief discussions are provided. The findings indicate that isolation of infected individuals in the human population helps to reduce disease transmission.

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Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible–Infectious–Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in the age of the populations concerned leads to considering models in age groups with specific susceptibilities, which makes the prediction problem more difficult. Basically, there are three age groups of interest which are, respectively, 0–19 years, 20–64 years, and >64 years, but in this article, we only consider two (20–64 years and >64 years) age groups because the group 0–19 years is widely seen as being less infected by the virus since this age group had a low infection rate throughout the pandemic era of this study, especially the countries under consideration. In this article, we proposed a new mathematical age-dependent (Susceptible–Infectious–Goneanewsusceptible–Recovered (SIGR)) model for the COVID-19 outbreak and performed some mathematical analyses by showing the positivity, boundedness, stability, existence, and uniqueness of the solution. We performed numerical simulations of the model with parameters from Kuwait, France, and Cameroon. We discuss the role of these different parameters used in the model; namely, vaccination on the epidemic dynamics. We open a new perspective of improving an age-dependent model and its application to observed data and parameters.

(1) Background: The estimation of daily reproduction numbers throughout the contagiousness period is rarely considered, and only their sum R0 is calculated to quantify the contagiousness level of an infectious disease. (2) Methods: We provide the equation of the discrete dynamics of the epidemic’s growth and obtain an estimation of the daily reproduction numbers by using a deconvolution technique on a series of new COVID-19 cases. (3) Results: We provide both simulation results and estimations for several countries and waves of the COVID-19 outbreak. (4) Discussion: We discuss the role of noise on the stability of the epidemic’s dynamics. (5) Conclusions: We consider the possibility of improving the estimation of the distribution of daily reproduction numbers during the contagiousness period by taking into account the heterogeneity due to several host age classes.

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(1) Background: Impact and severity of coronavirus pandemic on health infrastructure vary across countries. We examine the role percentage health expenditure plays in various countries in terms of their preparedness and see how countries improved their public health policy in the first and second wave of the coronavirus pandemic; (2) Methods: We considered the infectious period during the first and second wave of 195 countries with their current health expenditure as gross domestic product percentage (CHE/GDP). An exponential model was used to calculate the slope of the regression line while the ARIMA model was used to calculate the initial autocorrelation slope and also to forecast new cases for both waves. The relationship between epidemiologic and CHE/GDP data was used for processing ordinary least square multivariate modeling and classifying countries into different groups using PC analysis, K-means and hierarchical clustering; (3) Results: Results show that some countries with high CHE/GDP improved their public health strategy against virus during the second wave of the pandemic; (4) Conclusions: Results revealed that countries who spend more on health infrastructure improved in the tackling of the pandemic in the second wave as they were worst hit in the first wave. This research will help countries to decide on how to increase their CHE/GDP in order to properly tackle other pandemic waves of the present COVID-19 outbreak and future diseases that may occur. We are also opening up a debate on the crucial role socio-economic determinants play during the exponential phase of the pandemic modelling.

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