Tesis de doctorado en ciencias matemáticasInfectious diseases are caused by organisms, such as bacteria, viruses, parasites, or fungi, and can be transmitted from one person to another or by vectors [1]. These diseases have caused epidemics and pandemics throughout history and in our own time. For example, the Spanish u of 1918 is considered the worst pandemic that affected 500 million people, and it has been estimated between 17 and 50 million deaths worldwide [2]. Malaria is still an endemic disease in many African countries, but it has significantly decreased its mortality rate since 2000 [3]. Dengue is another endemic disease in more than 100 countries around the world, with the highest number of cases reported in 2019 [4]; particularly, more than 3.1 million dengue cases were reported in the Americas region during that year [5]. Currently, up to this document writing date, the COVID-19 pandemic has affected more than 100 million people worldwide and has caused the death of 2.2 million approximately [6]. These types of diseases do not only directly affect the health of individuals, but they also have an impact on the economy, resulting in significant losses [7]. For example, 170 million dollars approximately are spent by the Mexican government on dengue disease annually, without considering the long-term consequences of dengue, the impact on travel and tourism, among others [8]. Another example is COVID-19, which has caused serious damage to the world economy due to the strict measures implemented by governments to stop its spread [9]. Thus, these diseases are a serious public health problem, and their effects vary greatly by geographical area and populations, and low-income countries are the most affected[10].Universidad de Sonora. División de Ciencias Exactas y Naturales. Programa de Posgrado en Matemáticas; 2021.